cp's OEIS Frontend

A260591 a(n) is the number of odd numbers k < 2^n such that A260590(k) = n.

%I A260591 #72 Nov 28 2024 11:01:31
%S A260591 0,1,0,1,2,0,3,7,0,12,0,30,85,0,173,476,0,961,0,2652,8045,0,17637,
%T A260591 51033,0,108950,312455,0,663535,0,1900470,5936673,0,13472296,39993895,
%U A260591 0,87986917,0,257978502,820236724,0,1899474678,5723030586,0,12809477536,38036848410,0,84141805077,0,248369601964
%N A260591 a(n) is the number of odd numbers k < 2^n such that A260590(k) = n.
%C A260591 a(n) is either 0 or about c^(n-1) with c = log(3)/log(2).
%C A260591 Nonzero values give A100982. - _Ruud H.G. van Tol_, Nov 25 2021
%C A260591 A close variant of this sequence, that starts at offset 0, but with a(0)=0 and a(1)=1, maps it to the count of dropping patterns of 2^n+c(2^n), with the c(2^n) as mentioned with A177789. The positions of the zeros of that variant sequence might be a close variant of A054414, again with a(0)=0 (not properly checked yet). - _Ruud H.G. van Tol_, Nov 28 2021
%C A260591 It appears that the proportion of zeros is 1-log(2)/log(3) = 36.907...%. - _Jesse Randall_, Oct 10 2024
%e A260591 a(1) = 0 since there exists no odd number whose msa is 1;
%e A260591 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;
%e A260591 a(3) = 0 since there exists no odd number whose msa is 3;
%e A260591 a(4) = 1 since there is only one number, 1, less than 2^(4+1) whose msa is 4;
%e A260591 a(5) = 2 since there are two numbers, 11 & 23, less than 2^(4+1) whose msa is 4; etc.
%t A260591 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]
%Y A260591 Cf. A260590, A054414, A100982, A186009, A186008, A177789, A346640.
%K A260591 nonn
%O A260591 1,5
%A A260591 Joseph K. Horn, O. Praem, and _Robert G. Wilson v_, Jul 29 2015
%E A260591 a(31) onwards from _Jesse Randall_, Sep 09 2024