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A182660 a(2^(k+1)) = k; 0 everywhere else. 2
0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

A surjection N->N designed to spite a guesser who is trying to guess whether it's a surjection, using the following naive guessing method: Guess that (n0,...,nk) is a subsequence of a surjection iff it contains every natural less than log_2(k+1).

This sequence causes the would-be guesser to change his mind infinitely often.

a(0)=0. Assume a(0),...,a(n) have been defined.

If the above guesser guesses that (a(0),...,a(n)) IS the beginning of a surjective sequence, then let a(n+1)=0. Otherwise let a(n+1) be the least number not in (a(0),...,a(n)).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

S. Alexander, On Guessing Whether A Sequence Has A Certain Property, arXiv:1011.6626  [math.LO], 2010-2012.

S. Alexander, On Guessing Whether A Sequence Has A Certain Property, J. Int. Seq. 14 (2011) # 11.4.4.

PROG

(MAGMA) [ exists(t){ k: k in [1..Ceiling(Log(n+1))] | n eq 2^(k+1) } select t else 0: n in [0..100] ];

(PARI) A182660(n) = if(n<2, 0, my(p = 0, k = isprimepower(n, &p)); if(2==p, k-1, 0)); \\ Antti Karttunen, Jul 22 2018

CROSSREFS

Cf. A082691, A135416, A209229.

Sequence in context: A104261 A028702 A083929 * A286100 A338210 A122698

Adjacent sequences:  A182657 A182658 A182659 * A182661 A182662 A182663

KEYWORD

nonn

AUTHOR

Sam Alexander, Nov 27 2010

STATUS

approved

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Last modified October 26 05:25 EDT 2021. Contains 348256 sequences. (Running on oeis4.)