A182660 a(2^(k+1)) = k; 0 everywhere else.

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

Offset: 0

Author

Sam Alexander, Nov 27 2010

Keywords

• nonn

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.

Crossrefs

Cf. A082691, A135416, A209229.

Programs

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