Suggestions for A200000

("disclaimer": I created this page in a rush. Please complete by other suggestions that may have been sent to the seqfan list, and improve formatting if you can. Thanks in advance.)

Dear Seqfans,
On the Future Projects page on the OEIS wiki,
Charles Greathouse suggested that we reserve A200000
for an especially interesting sequence. Something really
special. Any suggestions?
(We can renumber any recent sequence to A200000, of course.)
— Neil, Sun, Nov 13, 2011 at 9:35 PM

Suggestions

A200066, Marks found on the Ishango bone in nondecreasing order

Dear Neil

I propose a sequence related to A100000.
A-NUMBER: A200000
NAME: Marks found on the Ishango bone in nondecreasing order.
DATA: 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 11, 13, 17, 19, 19, 21
OFFSET: 1
COMMENTS: The sequence has 16 terms: 10 primes and 6 composites. The repeated
numbers are primes: 5, 11, 19.
LINKS:
http://www.math.buffalo.edu/mad/Ancient-Africa/ishango_bone.jpg
CROSSREFS: A000040, A100000.
KEYWORD: nonn,fini,full,(nice?)
AUTHOR: OEIS

Best regards,
Omar E. Pol   (date stamp)

A169965, Numbers whose decimal expansion contains only 0's and 2's.

I propose http://oeis.org/A169965
Best,
É.
(TO DO: add complete signature)

A199339, Excess of prime numbers with even digit sum, among the first n primes

I agree with earlier statements about not chosing again the Ishango bone,
and that the selected sequence should correspond to a recent
mathematical finding.  

I googled "recent news in mathematics about integer sequences" or the like,
and among the results I found was
http://www.sciencedaily.com/releases/2010/05/100512172533.htm :

Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical
Proof of Hypothesis

ScienceDaily (May 12, 2010) — On average, there are as many prime
numbers for which the sum of decimal digits is even as prime numbers
for which it is odd. This hypothesis, first made in 1968, has recently
been proven by researchers from the Institut de Mathématiques de
Luminy (CNRS/Université de la Méditerranée).

When I checked I noticed that the corresponding sequence was not yet
in OEIS, and I just created

https://oeis.org/draft/A199339
Excess of prime numbers with even digit sum, among the first n primes.
1, 0, -1, -2, -1, 0, 1, 2, 1, 0, 1, 2, 1, 0, -1, 0, 1, 0, -1, 0, 1, 2,
1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, -1,
-2, -1, -2, -3, -4, -3, -2, -3, -2, -1, -2, -3, -2, -1, -2, -3, -2

I would not say that this is "something very special", but

* it was not yet in the OEIS,
- it refers to a recent result and, if I understand correctly,
- this recent result settles a "long standing" (>40yr) conjecture by a
well-known Mathematician (Golfand)

* il is somehow representative of OEIS because
- it's about primes, as many other sequences
- it's about digits, as many other sequences
- although it's "base", it has some nontrivial "serious" math behind.

So I suggest this to be (maybe) considered as a potential candidate.

Regards, — M. F. Hasler 20:00, 14 November 2011 (UTC)

The binary version, A200248, seems more mathematical. However, it was in the OEIS already, see A130911, and I had to recycle A200248. - N. J. A. Sloane, Nov 15 2011, Nov 17 2011

I agree! I simply did not have the time to read the paper but read that there might be exceptions in a few well-known cases, so I did not want to take the risk to chose base 2 in case this was one of the exceptions. — M. F. Hasler 16:44, 15 November 2011 (UTC)

Most interesting sequence among sequences containing 200000

I suggest  to reserve A200000 for the most interesting sequence among sequences containing 200000 (and not only among them!) 

In my opinion, it is a beautiful finite sequence A014778 by Yv. Babe, M. Protat and Ol. Gerard. 

Regards,
Vladimir Shevelev, Nov 14 2011

A198683, Number of distinct values taken by i^i^...^i [...]

There are other sequences pertaining to 2s, 3s, etc., with exponentiation carets and parentheses inserted, but this one about the imaginary unit was only recently added and it really surprises me it wasn't in the OEIS already. Alonso del Arte 23:27, 16 November 2011 (UTC)

A200265, Triangle read by rows: coefficients in an asymptotic expansion of the n-th prime

Juan Arias-de-Reyna proposes this for A200000 - see the pink comments in that entry. — N. J. A. Sloane, Nov 17 2011

What a nice sequence! Charles R Greathouse IV 07:26, 20 November 2011 (UTC)

A200216, Danilov's sequence of x obeying 0 < |x^3-y^2| < sqrt(x) with integer (x,y)

Artur Jasinski proposes this. He says: I'm give You sugestion on candidate sequence on A200000 number: A200216 I was find today very easy formula by Lucas numbers. This sequence is very important for Hall conjecture.

A200715

See A200715 from Jon Wild. It has several nice features - easily understood (once you figure out the rules), yet hard, with a nice illustration. And it comes from graph theory (or maybe complexity theory, or string theory!)

Neil