

A260591


a(n) = number of odd numbers k < 2^n such that A260590(k) = n.


0



0, 1, 0, 1, 2, 0, 3, 7, 0, 12, 0, 30, 85, 0, 173, 476, 0, 961, 0, 2652, 8045, 0, 17637, 51033, 0, 108950, 312455, 0, 663535, 0
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OFFSET

1,5


COMMENTS

a(n) is either 0 or about c^(n1) with c = log(3)/log(2).
Out of the first thirty terms, 12, or 40% are zeros.


LINKS

Table of n, a(n) for n=1..30.


EXAMPLE

a(1) = 0 since there exists no odd number whose msa is 1;
a(2) = 1 since there is only one odd number, 5 with k=2 2k+1, with k less than 2^2 whose msa is 2;
a(3) = 0 since there exists no odd number whose msa is 3;
a(4) = 1 since there is only one number, 1, less than 2^(4+1) whose msa is 4;
a(5) = 2 since there are two numbers, 11 & 23, less than 2^(4+1) whose msa is 4; etc.


MATHEMATICA

msa[n_] := If[ OddQ@ n, (3n + 1)/2, n/2]; f[n_] := Block[{k = 2n + 1}, Length@ NestWhileList[ msa@# &, k, # >= k &]  1]; g[n_] := Length@ Select[ Range[ 2^(n  1)], f@# == n &]; Array[ g, 20]


CROSSREFS

Cf. A260590.
Sequence in context: A021495 A332356 A309655 * A127160 A131330 A022833
Adjacent sequences: A260588 A260589 A260590 * A260592 A260593 A260594


KEYWORD

nonn,more


AUTHOR

Joseph K. Horn, O. Praem, and Robert G. Wilson v, Jul 29 2015


STATUS

approved



