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Hello, world! --Zak Seidov 05:13, 23 November 2010 (UTC)

Hello Zak! To answer your question: Yes, anyone can comment here! In case something ugly happens, you can revert to an earlier version (via the "history" tab). — M. F. Hasler 01:55, 29 November 2010 (UTC)

Contents

Early Birds in EKG A064413

Early Birds in EKG (A064413)

1. Numbers are given in order of their appearances in A064413.

2. From the first 888 EB's, 518 are even and 370 odd.

3. What is origin of two branches in the Figure?


File:EB_EKG.jpg

How to upload the file in your talk page

How to upload file?

1. First go to your user's page:

in my case

http://oeis.org/wiki/User_talk:Zak_Seidov

and

2. start a new section:

click "+" in the menu (or "alt-shift-+")

3. enter any head line your wish:

e.g.,

"How to upload the file in your talk page"

4. Start to print your talk:

(e.g., repeat your head line).

5. Now go to left panel find "Toolbox" and click "Upload file"

6. Click "Browse..." and find in your computer the file you need:

e.g., Figure, .txt etc. and

7. Click "Open".

8. Print in the "Destination file" window "new name" -

if you wish to change the original title to "public" one.

9. Click "Upload file" below.

If it's OK, your file is now in the OEIS WIKI.

Note that points 5 - 9 can be done quite independently from your section

(even from your talk page I guess).

10. Now in the place you wish in the your talk you print:

File:FileName.jpg

(of course FileName = name of your "public" name of uploaded file, e.g., Even EKG.jpg and


10. After clicking "Show preview"

you may check if everything looks OK for you

including the Figure:

File:Even EKG.jpg

and then

11. Click "Save page". (I guess that you can't do this "Save page" without first "Show preview".)

12. Remember that in any moment you and

- ugly moment of WIKI - anyone else :( can edit your talk.

13. I hope that someone may explain this better than me and put

"How to upload the file" in OEIS WIKI QandA.

Even terms in EKG (A064413)

From the first 10000 terms of A064413, 5189 are even and 4811 odd.

From the first 1000 terms of A064413, 524 are even and 478 odd.

Even terms of EKG with indices <=1000: {index in EKG, term} (notice dependence a(n) is very close to linear one a(n)=n)


File:Even_EKG.jpg

A138173: First 1000 terms

A138173 a(n) = smallest m such that m^3 begins with n^2.

(We might add also 0 because as 0^3 "begins' with 0^2.

In general, notice that for n=a^3 m=a^(2/3): a(1)=1, a(8)=4, a(27)=9, a(64)=16.

The mnemonic rule is: "if n is cube m is square"!

What about patterns in the Figures?

File:A138173 200.JPG





(Sub)sequences of distinct successive prime gaps

(See sequences A079007 and A079889.) — M. F. Hasler 14:40, 5 April 2013 (UTC)
(Sub)sequences of distinct successive prime gaps 
n - length of sequence of distinct successive prime gaps 
m - index of first prime of the sequence
p - prime(m) 
sn - sequences of n distinct successive prime gaps
{n,m,p,sn}
{1,2,3,{2}},
{2,1,2,{1,2}},
{3,7,17,{2,4,6}},
{4,23,83,{6,8,4,2}},
{5,30,113,{14,4,6,2,10}},
{6,94,491,{8,4,6,12,2,18}},
{7,219,1367,{6,8,18,10,14,4,2}},
{8,279,1801,{10,12,8,16,14,6,4,2}},
{9,773,5869,{10,2,16,6,20,4,12,14,28}},
{10,1856,15919,{4,14,22,12,2,18,10,6,26,24}},
{11,3724,34883,{14,16,6,20,10,12,2,18,42,4,24}},
{12,6999,70639,{18,6,4,20,22,8,12,24,16,14,10,30}},
{13,7000,70657,{6,4,20,22,8,12,24,16,14,10,30,18,2}},
{14,19205,214867,{16,8,22,26,4,24,20,6,58,12,14,10,36,18}},
{15,19205,214867,{16,8,22,26,4,24,20,6,58,12,14,10,36,18,2}},
{16,184163,2515871,{2,6,18,10,14,30,16,54,36,20,12,34,74,4,8,24}},
{17,280103,3952733,{26,4,8,42,60,36,10,18,30,14,16,12,2,6,34,20,22}},
{18,849876,13010143,{4,12,32,6,16,80,24,22,72,8,28,30,84,2,46,14,10,26}},
{19,1870722,30220163,{8,36,12,54,4,50,16,18,26,10,32,28,14,22,6,2,70,20,42}}

Two more terms from David Newman:
{20,3570761,60155567,{30,14,48,28,56,16,2,46,12,38,4,6,32,24,10,18,8,22,20,36}}
{21,4114341,69931991,{2,10,8,30,18,22,32,16,42,36,20,46,6,44,48,40,26,12,54,4,50}}

More terms:
{22,11271072, 203674907,{30,12,20,24,4,32,34,14,16,6,62,18,22,8,58,42,38,40,2,10,48,26}}
{23,55282774,1092101119,{48,24,30,58,20,4,74,52,12,2,114,22,18,42,44,10,8,36,46,56,90,28,6}}
{24,68256040,1363592621,{56,10,2,84,30,58,8,60,18,12,54,24,52,42,20,96,4,26,46,14,22,32,6,40}}
{25,68256041,1363592677,{10,2,84,30,58,8,60,18,12,54,24,52,42,20,96,4,26,46,14,22,32,6,40,56,16}}
{26,104011359,2124140323,{48,40,152,46,2,28,14,4,72,12,20,58,140,78,30,16,56,42,10,6,62,60,34,36,24,108}}

Difference between neighbor terms not less than d

Difference between neighbor primes not less than d (say,d=100)
a(n) = smallest prime p not in the sequence such that |p-a|>=d; 
case d=100, a(1)=2;

First terms (from 1001 calculated):   
2,103,3,107,5,109,7,113,11,127,13,131,17,137,19,139,23,149,29,151,31,157 
Fixed points:
2,239,409,757,971,1217,1471,1667,1907,1997,2273,2441,2579,2903,3089,
3319,3373,3511,3733,3917,4003,4211,4373,4597,4637,4931,5171,5351,5399,
5431,5657,5857,6079,6269,6551,6977,7193,7457,7741.

First 300 terms of A025415

First 300 terms of A025415 Least sum of 3 distinct nonzero squares in exactly n ways.

{{1,14},{2,62},{3,101},{4,161},{5,206},{6,314},{7,341},{8,446},{9,689},{10,734},{11,854},{12,1106 200 triples {x, y, z}, 0 < x < y < z, such that x^2 + y^2 + z^2 = 176294 = A025415(200)

{2, 27, 419}, {2, 49, 417}, {2, 153, 391}, {2, 211, 363}, {2, 221, 357

Sum and difference of semiprimes are semiprimes.

Least pair is (10, 4): 14 and 6 both sp.

More n's s.t. n +/- are sp: 10, 91, 115, 119, 205, 209, 213, 217, 291, 295, 299, 305, 323, 407, 411, 485, 489, 493, 497, 501, 515, 533, 685, 699, 703, 717, 749, 767, 785, 789, 803, 917, 955, 989, 1007, 1077, 1115, 1137, 1141, 1145, 1195, 1199, 1203, 1207, 1257, 1267, 1333, 1343, 1347, 1351, 1383, 1387, 1389, 1393, 1397, 1401, 1461, 1465, 1469, 1473, 1513, 1565, 1685, 1707, 1731, 1735, 1761, 1765, 1799, 1803, 1839, 1853, 1919, 1923, 1941, 1963, 1981

All are odd (except of 10) as, for even n, one of (n-4, 4, n+4) is devisible by 3 and hence by 6 (and can't be sp).

A220952: Some trivial observations

A220952 Some trivial observation(s):

parities of a(n) and n are the same (hence first differences are odd)

sequence is rearrangement of non-negative integers

for odd squares n's a(n)=2n-1(?)

Look also at (symmetric) graph of abs(a(n)-n):

File:AA.gif

...nothing fascinating yet :(

A225752: failed submission

Just to keep in history... one of my (many) withdrawn submissions A225752 allocated for Zak Seidov (history; edit; published version)

  1. 4 by Zak Seidov at Tue May 14 13:28:01 EDT 2013

NAME a(n) = number of prime digits (2,3,5,7) in (decimal representation of) n^2. allocated for Zak Seidov DATA 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 2, 1, 2, 1, 0, 0, 0, 2, 2, 2, 1, 2, 1, 0, 0, 0, 1, 0, 1, 3, 1, 1, 0, 2, 0, 0, 1, 0, 1, 3, 1, 2, 2, 1, 2, 1, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 1, 0, 3, 2, 0, 1, 1, 0, 1, 1, 3, 2, 3, 3, 2, 0, 1, 0, 1, 2, 0, 2, 4, 2, 2, 2, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 3, 2, 2, 1, 4, 2, 1, 2, 0, 0, 0, 0, 2, 3, 3, 2, 1, 1, 0, 0, 1 OFFSET 1,5 COMMENTS The sequence is unbound. EXAMPLE The first non-zero term is a(5) = 2 because 5^2 = 25 (2 prime digits); a(6) = 1 because 6^2 = 36 (1 prime digit). MATHEMATICA Table[id = IntegerDigits[n^2]; Sum[Count[id, x], {x, {2, 3, 5, 7}}], {n, 150}] CROSSREFS Cf. A191486 Squares using only the prime digits (2, 3, 5, 7). A030485 Squares composed of digits {2, 5, 7}. KEYWORD nonn,changed allocated AUTHOR Zak Seidov, May 14 2013 STATUS proposed approved

  1. 3 by Zak Seidov at Tue May 14 08:57:14 EDT 2013

STATUS editing proposed Discussion Tue May 14 13:13 Joerg Arndt: "base" (and, to add some opinion, contrived). 13:43 Charles R Greathouse IV: Can we have a capsule proof that it is unbounded? A naive counting argument won't work, since the set of primes is 'smaller' than the set of numbers composed of nonprime digits.

  1. 2 by Zak Seidov at Tue May 14 08:56:19 EDT 2013

NAME allocateda(n) = number of prime fordigits (2,3,5,7) in (decimal Zakrepresentation Seidovof) n^2. DATA 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 2, 1, 2, 1, 0, 0, 0, 2, 2, 2, 1, 2, 1, 0, 0, 0, 1, 0, 1, 3, 1, 1, 0, 2, 0, 0, 1, 0, 1, 3, 1, 2, 2, 1, 2, 1, 2, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 1, 0, 3, 2, 0, 1, 1, 0, 1, 1, 3, 2, 3, 3, 2, 0, 1, 0, 1, 2, 0, 2, 4, 2, 2, 2, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 3, 2, 2, 1, 4, 2, 1, 2, 0, 0, 0, 0, 2, 3, 3, 2, 1, 1, 0, 0, 1 OFFSET 1,5 COMMENTS The sequence is unbound. EXAMPLE The first non-zero term is a(5) = 2 because 5^2 = 25 (2 prime digits); a(6) = 1 because 6^2 = 36 (1 prime digit). MATHEMATICA Table[id = IntegerDigits[n^2]; Sum[Count[id, x], {x, {2, 3, 5, 7}}], {n, 150}] CROSSREFS Cf. A191486 Squares using only the prime digits (2, 3, 5, 7). A030485 Squares composed of digits {2, 5, 7}. KEYWORD allocated nonn AUTHOR Zak Seidov, May 14 2013 STATUS approved editing

How to save large result of search in OEIS?

Sorry, I couldn't put this Q in Q/A page - tricky thing to me :(

If I have many-pages of search results in OEIS (and I need only data format) -

how can I save it in my notebook (as .txt file) to further working off-line? Thanks!

Interesting links

http://www.pbs.org/wgbh/nova/physics/prime-questions.html

https://twitter.com/ZakSeidov

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