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# Template talk:Sequence of the Day

## Intentional or coincidence!?

The first Sequence of the Day appeared on 10 Oct 2010 (10/10/10 in decimal, 1010/1010/1010 in binary!) which happens to be Neil Sloane's birthday! Was it intentional or coincidence!? Or was it that the coolness of that decimal/binary date was the motivating factor in starting Sequence of the Day and it so happens that Oct 10 (10/10 in decimal, 1010/1010 in binary!) is Neil Sloane's birthday!? — Daniel Forgues 15:41, 12 October 2010 (UTC)

It was a huge coincidence. It was the birthday of Dean Robert Thomas as it was announced by Prof. Brender that actually motivated this; he called it a "perfect binary day." I didn't know Neil's birthday was also on that day. The personal thing that I asked Neil for the article on the 100K party in the South End was whether or not he had a car with more than 100K miles on it. — Alonso del Arte 15:55, 12 October 2010 (UTC)

## Next OEIS Wiki contributor

### For 15 Oct 2010

An invitation had been sent, but has not been confirmed; it's true that it cannot (or should not) be expected to have the time to do it within 2 days only. It seems a good idea to fix a list of volunteers for, let's say, at least one week ahead.

P.S.:

• is it reasonable to have this list in reverse chronological order?
• didn't I read somwhere that there should be no log of the editors except for the pages "history"? ;) — M. F. Hasler 03:23, 15 October 2010 (UTC)
In regards to "there should be no log of the editors except for the pages "history"," that's not a rule, and maybe it was a dumb idea anyway (I can say that since that particular bit was my idea). The point of it was to avoid this feature of the OEIS Wiki getting bogged down in rules and procedures at the expense of substance. But it's becoming clearer to me that some procedure (nothing tremendously rigid) is a good thing. — Alonso del Arte 04:50, 15 October 2010 (UTC)
Thank you, Alonso, for filling in the gap of Oct.15 ... — M. F. Hasler 12:59, 15 October 2010 (UTC)

### For 14 Oct 2010

I invited Maximilian Hasler to write Sequence of the Day for 14 Oct 2010. Here is his draft. — Jaume Oliver Lafont 13:52, 13 October 2010 (UTC)

As you can see, I chose A057652, but now I realized that either {1,2} should be added in front of the given values, or "n>2" should be added in the definition. For the moment being, I did the second thing, but only on the "sequence of the day" version. Any comments/suggestions are welcome. — M. F. Hasler 14:30, 13 October 2010 (UTC)

### For 13 Oct 2010

I invited (yesterday) Jaume Oliver Lafont to write Sequence of the Day for 13 Oct 2010. — Daniel Forgues 17:39, 12 October 2010 (UTC)

## Future (next 2 months) OEIS Wiki contributors to SoD

Or maybe we should do self-selection going about a month in advance. It has also been suggested that we have a back-up sequence just in case. I'm thinking sequences with keyword:base and keyword:nice for that purpose. — Alonso del Arte 02:11, 15 October 2010 (UTC)

Why keyword:base? These refer to base-dependent integer sequences, which have much less number theoretic interest than base-independent integer sequences... — Daniel Forgues 20:48, 16 October 2010 (UTC)
Exactly perfect for a back-up SOD. Uninteresting enough to encourage continued contribution, but easy enough to understand that a write-up can be done in a hurry without requiring too much pondering. Alonso del Arte 00:13, 20 October 2010 (UTC)

The following list of OEIS Wiki contributors to the Sequence of the Day is in reverse chronological order of year and month.

### February 2011

OEIS Wiki contributors for February 2011 Sequence of the Day
Date[1] OEIS Wiki contributor Sequence of the Day Comment
1  Charles R Greathouse IV A181437 Size of the longest increasing sequence of primes starting with 2, 3 and with second order differences bounded by n.
2   A??????
3   A??????
4   A??????
5   A??????
6   A??????
7   A??????
8   A??????
9  Charles R Greathouse IV A180442 Numbers n such that a sum of two or more consecutive squares beginning with n^2 is a square. Bremner, Stroeker, & Tzanakis, On Sums of Consecutive Squares, 1991.
10   A??????
11   A??????
12   A??????
13   A??????
14   A??????
15  Charles R Greathouse IV A068315 Numbers n such that A025474(n) > 1 and A025474(n+1) > 1. Sequence gives A025474(n).
16   A??????
17  Charles R Greathouse IV A063789 Largest prime gap between n^2 and (n + 1)^2.
18   A??????
19   A??????
20   A??????
21   A??????
22   A??????
23   A??????
24 Charles R Greathouse IV A000019 Number of primitive permutation groups of degree n.
25   A??????
26   A??????
27   A??????
28   A??????

1. By the date is a link to the last edit of SoD for the given date.

### January 2011

OEIS Wiki contributors for January 2011 Sequence of the Day
Date[1] OEIS Wiki contributor Sequence of the Day Comment
1  Karsten Meyer A181780 Numbers ${\displaystyle \scriptstyle n\,}$ which are Fermat pseudoprimes to some base ${\displaystyle \scriptstyle b,\,2\,\leq \,b\,\leq \,n-2\,}$. New Year's Day.

Prime year, previous was 2003, next is 2017.

2  Daniel Forgues A127338 Numbers that are the sum of 11 consecutive primes. 2011 = 157+163+167+173+179+181+191+193+197+199+211 (a prime that is the sum of 11 consecutive primes ending at 211)
3   A??????
4   A??????
5   A??????
6   A??????
7   A??????
8   A??????
9   A??????
10   A??????
11   A??????
12   A??????
13   A??????
14   A??????
15   A??????
16   A??????
17 A?????? Martin Luther King Jr. Day
18   A??????
19   A??????
20  Charles R Greathouse IV A156695 Odd numbers which are not of the form ${\displaystyle \scriptstyle p+2^{a}+2^{b},\,a,\,b\,>\,0,\,p\,}$ prime.
21   A??????
22   A??????
23   A??????
24   A??????
25   A??????
26   A??????
27   A??????
28   A??????
29   A??????
30   A??????
31   A??????

1. By the date is a link to the last edit of SoD for the given date.

## Previous (last few months) OEIS Wiki contributors to SoD

Eventually, when this section gets too big, we may create a separate page Sequence of the Day (archive). — Daniel Forgues 03:29, 8 November 2010 (UTC)

Sequence of the Day (archive) created to reduce clutter on current page for SoD. — Daniel Forgues 04:32, 1 February 2011 (UTC)

### December 2010

On some day I must've gotten confused and thought there had been no SOTD for that day when I had put one in already. But if we can delete one of these post facto, the best candidate would be A40 (the primes). Alonso del Arte 18:52, 30 December 2010 (UTC)

OK, I'll remove A000040 from Dec 18, thus allowing to move to next day alls sequences from the second Dec 6 sequence to the Dec 17 sequence, which has the added benefit of putting Beethoven's sequence on Dec 17 (Beethoven's birthday.) — Daniel Forgues 04:34, 1 January 2011 (UTC)
OEIS Wiki contributors for December 2010 Sequence of the Day
Date[1] OEIS Wiki contributor Sequence of the Day Comment
1  Alonso del Arte A025547 Least common multiples of the first ${\displaystyle \scriptstyle n\,}$ odd numbers. Birthday of Martin Heinrich Klaproth.
2  Alonso del Arte A007598 Squares of the Fibonacci numbers ${\displaystyle \scriptstyle {F_{n}}^{2}\,}$.
3  Alonso del Arte A066716 The binary Champernowne constant.
4  Alonso del Arte A181832 The product of the positive integers ${\displaystyle \scriptstyle i\,\leq \,n\,}$ that are strongly prime to ${\displaystyle \scriptstyle n,\ n\,\geq \,0\,}$. phitorial(n) / divisorial(n - 1).
5  Alonso del Arte A033168 An arithmetic progression of primes.
6  Alonso del Arte A061909 Base 10 skinny numbers.
7  Alonso del Arte A051802 Nonzero multiplicative digital root of ${\displaystyle \scriptstyle n\,}$.
8  Alonso del Arte A051250 Numbers whose reduced residue system consists of 1 and prime powers only. Reinhard Zumkeller has conjectured that this sequence is finite and given in full.
9  Alonso del Arte A038136 Dihedral calculator primes.
10  Alonso del Arte A006037 Weird numbers. Abundant numbers which are not pseudoperfect numbers.
11  Alonso del Arte A114645 The numbers ${\displaystyle \scriptstyle 2^{n}-1\,}$ written in groups of three digits, with leading zeros omitted.
12  Alonso del Arte A005224 Aronson's sequence. Cf. Self-referential assertions.
13  Alonso del Arte A027606 Natural logarithm base ${\displaystyle e}$ in the duodecimal numeral system.
14  Alonso del Arte A093341 Decimal expansion of "lemniscate case".
15  Alonso del Arte A065421 Decimal expansion of the twin primes Brun's constant ${\displaystyle \scriptstyle B_{2}\,}$: ${\displaystyle \scriptstyle \sum {\frac {1}{p}}+{\frac {1}{q}}\,}$ as ${\displaystyle \scriptstyle (p,q)\,}$ runs through the twin primes.
16  Alonso del Arte A014549 Gauß's constant ${\displaystyle \scriptstyle {\frac {2}{\pi }}\int _{0}^{1}{\frac {1}{\sqrt {1-x^{4}}}}dx\,}$. This is the reciprocal of the arithmetic-geometric mean of 1 and ${\displaystyle \scriptstyle {\sqrt {2}}\,}$.
17  Alonso del Arte A054245 Beethoven's Symphony No. 5 in C minor. Beethoven's birthday.
18  Alonso del Arte A182809 Fibonacci numbers that are base 10 cyclops numbers.
19  Alonso del Arte A053169 ${\displaystyle \scriptstyle n\,}$ is in this sequence if and only if ${\displaystyle \scriptstyle n\,}$ is not in sequence ${\displaystyle \scriptstyle A_{n}\,}$ in the database.
20  Alonso del Arte A038772 Numbers not divisible by any of their base 10 digits.
21  Alonso del Arte A080790 Binary emirps.
22  Alonso del Arte A105999 Vos Post's semiprimeth recurrence. From Wilson's primeth recurrence (Cf. A007097) idea.
23  Alonso del Arte A092447 Concatenate odd primes in decreasing order.
24  Alonso del Arte A143212 Row sums of the Fibonacci multiplication table. Christmas Eve.
25  Alonso del Arte A000292 Tetrahedral numbers Christmas.
26  Matthijs Coster A067097 Floor[X/Y] where X = concatenation in increasing order of first n powers of 2 and Y = that of first n natural numbers. Boxing Day, note that 20101226 appears in A067097.

Amarnath Murthy wondered in 2002 what happened to the integral parts of the quotients of these sequences?

27  Alonso del Arte A113307 Trott's third constant: decimal expansion coincides with its non-simple continued fraction read serially. Michael Trott found two other such constants.
28  Alonso del Arte A060295 Ramanujan's constant ${\displaystyle \scriptstyle e^{\pi {\sqrt {163}}}\,}$ Cf. Almost integers.
29  Alonso del Arte A008884 Collatz trajectory starting at 27 (see Collatz problem.)
30  Alonso del Arte A079397 Smallest prime recalling ${\displaystyle \scriptstyle n\,}$ previous primes in its base 10 representation.
31 None None New Year's Eve.

1. By the date is a link to the last edit of SoD for the given date.

## David W. Wilson's program for lucky numbers

Computing lucky numbers A000959 by the sieving process is space and time intensive because you have to store and sieve out the numbers you don't want. Here I present a "virtual sieve" algorithm implemented in C++ that generates n lucky numbers in order in real time, using just an O(n) array for the lucky numbers themselves + O(1) space.

#include <iostream>
using namespace std;
typedef unsigned long long int ulong;

//======================================================================
// This function generates a b-file for the lucky numbers (A000959)
// Run "lucky <elems>" to print elements 1 through <elems>
// It uses a "virtual sieve" and requires O(<elems>) space
// It runs as fast of faster than an explicit sieving algorithm
int main(int argc, char* argv[])
{
// Obtain number of elements from command line
ulong elems = argc <= 1 ? 1 : atoi(argv[1]);

// Create the sequence buffer
ulong* lucky = new ulong[elems];
if (lucky == NULL) {
cerr << "Too many elements requested" << endl;
return(1);
}

// Set first two elements explicitly
// Indexing from 0 simplifies the computation
lucky[0] = 1;
lucky[1] = 3;
if (elems >= 1) cout << "1 1" << endl;
if (elems >= 2) cout << "2 3" << endl;

// g is the largest index with lucky[g] <= n+1
ulong g = 0;

// Compute the nth lucky number for 2 <= n <= elems
for (ulong n = 2, g = 0; n < elems; n++) {

// Update g to largest index with lucky[g] <= n+1
if (lucky[g+1] <= n+1) g++;

// Now we are going to trace the position k of the nth
// lucky number backwards through the sieving process.
// k is the nth lucky number, so it is at position n
// after all the sieves.
ulong k = n;

// If lucky[i] > n+1, the sieve on lucky[i] does not alter
// the position of the nth lucky number, that is, does not
// alter k. So we need to run backwards through the sieves
// for which lucky[i] <= n+1. The last such sieve is the
// sieve for lucky[g], by definition of g.

// So, we run backwards through the sieves for lucky[g]
// down to the sieve for lucky[1] = 3.
for (ulong i = g; i > 0; i--) {

// Here k is the position of the nth lucky number
// after the sieve on lucky[i]. Adjust the position
// prior to the sieve on lucky[i].
k = k*lucky[i]/(lucky[i]-1);
}

// Here k is the position of the nth lucky number prior to
// sieve on 3, that is, after the sieve on 2. Adjust the
// position prior to the sieve on 2.
k = 2*k;

// Here k is the position of the nth lucky number prior to
// the sieve on 2, that is, within the natural numbers
// (1, 2, 3, ...) indexed on 0. So the nth lucky number is
lucky[n] = k+1;

// Adjust n for 1-indexing and print our new value
cout << n+1 << " " << lucky[n] << endl;
}

// Delete our array
delete[] lucky;

// And we are done
return 0;
}


— Please sign with ~~~~ (4 tildes) to automatically generate a timed (UTC)/dated signature. By the way, there are two OEIS Wiki contributors named David Wilson: User:David_J_Wilson and User:David_W._Wilson, so it's not clear who proposed the Lucky numbers program...

I copied your program into the Lucky numbers page. — Daniel Forgues 20:44, 17 October 2010 (UTC)
David W. Wilson. He put it in the S.O.D. write-up, so when I changed the Sequence of the Day to one for which it was no longer relevant, I deleted it from there. David will probably do a write-up one of these days but we'll have to clear the obstacle that he's not awake around 0:00. — Alonso del Arte 21:28, 17 October 2010 (UTC)
May we delete this section or should we keep it? (I put a link to the program in the comment in table above) — Daniel Forgues 01:35, 20 October 2010 (UTC)

## Keeping Track of Previous Sequences

I think it would be useful to remember recent sequences so that there is no repetition. Should we just write the sequence number after the author of the day? Then we can use a simple search to determine whether a sequence has already occurred. — T. D. Noe 20:53, 19 October 2010 (UTC)

Absolutely. That's probably a good idea before it gets too unwieldy. I'll do it for my own selections in a minute. — Alonso del Arte 21:23, 19 October 2010 (UTC)

## why is "noinclude" included ?

I think we should get rid of all the stuff that follows the "true content" of the SOTD, it's somehow unpleasant to see all of this "internal" stuff", which should not be disclosed to the average user. I suggest that at the bottom of the SOTD page a simple link should be added, pointing to another page which contains the "further information about the "sequence of the day" -- maybe simply put that information on the top of the "Talk" page ? — M. F. Hasler 16:39, 31 October 2010 (UTC)

That's because the average user should see the SOTD transcluded on another page, like perhaps the Main Page. To get an idea of how that might look, there is my test page as well as one Associate Editor's user page. — Alonso del Arte 16:41, 1 November 2010 (UTC)
--> Charles R Greathouse IV 06:03, 1 February 2011 (UTC)

Using the template {{oeis|A000040}} (e.g. A000040) to link to sequence pages instead of [[OEIS:A000040]] (e.g. A000040,) or [[OEIS:A000040|A000040]] (e.g. A000040) to omit displaying the prefix, is more convenient (and flexible) if we don't want to display the OEIS: prefix. Should we use the template throughout and avoid displaying the OEIS:prefix on links to sequence pages or do we want to keep the prefix visible to emphasize the fact that the sequence pages are not in the wiki? Also, if the sequence pages are ever moved in the future (e.g. from oeis.org/ to oeis.org/en/ for the english version, oeis.org/fr/ for the french version...) by merely updating the template all the links to sequence pages will be working again (actually the template is not necessary for this since the OEIS: prefix functionality can be updated...) — Daniel Forgues 17:27, 18 November 2010 (UTC)

I strongly favor hiding the prefix, and I support the {{oeis}} template for doing that. — Charles R Greathouse IV 06:03, 1 February 2011 (UTC)
Be careful with templates where they are not strictly necessary as in [[OEIS:A000040|]] rendered as A000040 vs. {{oeis|A000040}} rendered as A000040 (identical as of today). If a template is used by other templates in thousands of pages it constitutes an attack vector for spammers — unless the template is protected, but protection has its own administrative drawbacks. –Frank Ellermann 08:11, 9 August 2011 (UTC)
The wiki software has been changed so that a simple A000040 is sufficient to link to a sequence page. This is now the preferred way to refer to a sequence. In addition, when using OEIS interwiki links (as in [[OEIS:A000040|A000040]]) the OEIS: prefix is automatically suppressed. David Applegate 03:37, 28 September 2011 (UTC)

## Proposal for the overhaul of Sequence of the Day

As I've thought more about it, I think my original proposal for this was too loose and freewheeling. But at the same time I want to avoid an overly complicated bureaucracy. I think the best way to accomplish this is to use a mechanism that closely mirrors a procedure we have all become familiar with: that of reviewing and approving sequences in the first place. The new proposal (described below) I hope won't be a burden at all to the Associate Editors, which are numerous enough to have a different one of them review an upcoming Sequence of the Day each day, and only a small burden to the Editors in Chief. — Alonso del Arte 01:17, 1 March 2011 (UTC)

1. Any OEIS contributor can enter a draft for a Sequence of the Day at least 3 months in advance in a template page to be named in a consistent format. This can be like Template:Sequence of the Day for February 29‎, or if need be, [[Template:Sequence of the Day for 0229]]
2. Any OEIS Associate Editor can review or reject a draft at least 2 months in advance. If the draft is reviewed, the Associate Editor semi-protects the page.
3. Any OEIS Editor in Chief can approve or reject a reviewed draft at least a month in advance. If the draft is approved, the Editor in Chief fully protects the page.
4. On the appropriate day, at 00:00, a bot changes the Sequence of the Day accordingly (hence the need for a consistent naming format).
At the moment the problem is lack of submissions -- I count 8 in the last two months, or one per week for the sequence of the "day". This proposal would seem to make more sense if our trouble was editors tripping over each other to post...
That said, I'm not opposed to the general idea. I would simplify the procedure somewhat, removing the EiC step: I trust the Associate Editors to make sensible choices and protection seems counterproductive (errors are a much larger problem than vandalism).
Charles R Greathouse IV 10:47, 1 March 2011 (UTC)
You among those eight, thank you, Charles. But most of the people who've rejected doing one is because they felt put on the spot: "Come up with a write-up in the next 24 hours!" (David Applegate reacted like I had asked him to punch himself in the face, but that's a different story). If the Sequence of the Day I'm asking them to write is at least three months down the line, and there's some kind of review process, then they will (I hope) be more willing to do it. In my experience, mathematicians like to think a long time even for the simplest questions. — Alonso del Arte 15:50, 3 March 2011 (UTC)
Tomorrow I'll put this proposal to the SeqFan list, along with your suggestion to remove the third step. Alonso del Arte 23:20, 6 March 2011 (UTC)
Of course not putting people on the spot is good, though I'm not sure if the process is workable -- will someone write a bot to do step 4? Will an EiC actually do step #3? Will an AE actually do step #2? etc.
But I'm game to try it out. Would the current freewheeling system will still be in place for days when no one has gone through the process?
Charles R Greathouse IV 23:32, 6 March 2011 (UTC)
The bot is the least of my worries, even though I don't know the nuts and bolts of programming it. I figure it just needs to know how to access the server clock, the names of the months of the year, how many days each has, and how to deal with leap years. The people questions, those are the ones that worry me. Alonso del Arte 00:02, 7 March 2011 (UTC)

## OEIS Wiki clock (defined as OEIS Wiki server time, i.e. Eastern Time) or UTC?

Ideally this will be changed each day at 0:00 per the OEIS Wiki clock. (defined as OEIS Wiki server time, i.e. Eastern Time)

Today you mentioned

The Sequence of the Day will be relaunched June 28, 2011 with a new selection posted every day at 0:00 UTC.

Daniel Forgues 21:00, 6 June 2011 (UTC)

Already mentioned on the main page talk, it would be no problem to replace {{CURRENTMONTHNAME}} {{CURRENTDAY}} (UTC) by {{LOCALMONTHNAME}} {{LOCALDAY}} in {{Sequence of the Day/today}}. To be on the safe side wrt i18n local month names could be replaced by a {{#switch:{{LOCALMONTH}}|…}} construct to get English month names. –Frank Ellermann 01:10, 7 August 2011 (UTC)
{{fullmonth}} does something in this direction, but admittedly I don't see where the {{fullmonth|{{CURRENTMONTH}}}} in SotD would ever differ from a simpler {{CURRENTMONTHNAME}}. –Frank Ellermann 08:20, 9 August 2011 (UTC)
Now, {{Sequence of the Day/today}} has a parameter for the time zone, UTC (default) or LOCAL (OEIS Wiki server time zone.) — Daniel Forgues 16:57, 9 August 2011 (UTC)
Do we need the UTC feature? I had a vague idea to add a talk wikilink to the talk page of the SotD, for comments about today's SotD. With the UTC #switch magic that could be hard to read — but I'm not trying it today. –Frank Ellermann 01:52, 15 August 2011 (UTC)
I've removed it, UTC or rather CURRENT… is still the default, and an optional LOCAL parameter still triggers LOCAL… dates. There is now a talk link to discuss today's sequence on its talk page. –Frank Ellermann 01:43, 16 August 2011 (UTC)

## Archiving and drafting

Hi, I don't know how you plan to do this, just in case my € 0,02: If you want to archive a sequence of the day MMM DD you can copy or move it to a subpage MMM DD/YYYY. Likewise you could put drafts on subpages MMM DD/YYYY for future date(s) YYYY MMM DD — for popular dates there might be more than one future draft. Ideally there should be a working sequence of the day for all dates incl. February 29, and if last year's incarnation is boring a new draft can be created and go through the approval process when folks feel like it. As long as there is no new draft (or it wasn't approved) simply recycle the last SotD for a given date.

If you already know that you would prefer no SotD instead of silently recycling the old SotD, as it's apparently the case for July 4, just move it to a July 4/2011 subpage — for the purposes of {{Sequence of the Day/today}} that would trigger its "missing SotD" fallback on 2012-07-04. –Frank Ellermann 01:43, 7 August 2011 (UTC)

That might be a better idea.
As for the Sequence of the Day for July 4, 2011, Charles did not really like it, so we need a different one for July 4, 2012. But I wouldn't worry about that until March 2012.
I don't know if you've seen Template:Sequence of the Day for February 30. I doubt we'll have a February 30 again at any point in our lifetimes. Alonso del Arte 20:19, 7 August 2011 (UTC)
Nice, meanwhile I learned that there actually was a 1712-02-30 in Sweden, when they got their cute Julian to Gregorian calendar transition wrong, and "reverted" the error on 1712-02-30 (no ISO 8601 date, obviously :-) –Frank Ellermann 07:49, 9 August 2011 (UTC)