RE: [math-fun] more challenge sequences needed
Rich suggested A_n[n]+1. That is A037181, and a lot of terms are already known! Other similar sequences can be found in the Index to the OEIS under "diagonal sequences": diagonal sequences: A031135*, A037181, A031214, A051070, A091967, A102288 Neil
On 5/25/05, N. J. A. Sloane <njas@research.att.com> wrote:
Rich suggested A_n[n]+1.
That is A037181, and a lot of terms are already known!
Wow -- and GIMPS might plausibly spit out A000043[43] sometime soon! I suppose at that point A000047[47] would be the sticking point. (A000047[n] := Number of integers <= 2^n of form x^2 - 2y^2.) This is a theological question, Neil, but is A037181[42] correct? A000042[n] is named "n in unary", i.e. 1111....1. If you believe that this sequence "really" contains the number n just written oddly, then A000042[42]+1 is 43 -- after all, the numbers in A037181 aren't written in a funny base. On the other hand, if you believe that A000042[n] is (10^n - 1)/9 -- which is what its formula claims -- then A000042[42]+1 is 111...112. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
Michael, thanks very much for drawing my attention to the unsatisfactory state of those diagonal sequences! there were several errors, and I have redone them all. (New version in about 10 mins) here is a summary: diagonal sequences: A051070 = A_n(n) respecting the offset, A091967 = A_n(n) ignoring off set, A107357 = 1 + A_n(n) respecting offset, A102288 = 1 + A_n(n) ignoring offset diagonal sequences: incorrect versions: A031135, A037181 diagonal sequences: see also A102288 All 4 of the main sequences are now stuck, waiting for the 43rd Mersenne prime. Neil
participants (2)
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Michael Kleber -
N. J. A. Sloane