cp's OEIS Frontend

A229122 For odd m, let f(m) be the odd part of 3*m+1. a(n) is the least positive number of f-iterations of 2*n-1 to reach an odious number (A000069), or 0 if no such number of f-iterations exists.

%I A229122 #18 Jun 24 2023 13:07:23
%S A229122 1,2,1,1,1,2,2,2,1,2,1,1,1,1,1,1,1,3,1,1,1,2,2,2,1,3,2,3,3,2,2,2,1,2,
%T A229122 1,1,1,3,2,2,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,
%U A229122 1,2,3,4,1,4,1,1,1,1,1,1,1,3,1,1,1,2,2
%N A229122 For odd m, let f(m) be the odd part of 3*m+1. a(n) is the least positive number of f-iterations of 2*n-1 to reach an odious number (A000069), or 0 if no such number of f-iterations exists.
%C A229122 Since 1 is odious number, the conjecture that all a(n) > 0 is a very weak form of the "3x+1" (Collatz) conjecture.
%C A229122 We conjecture that this sequence is unbounded.
%e A229122 For n = 26, 2*n - 1 = 51; f(51) = 77 is evil; f(77) = 29 is evil; f(29) = 11 is odious, so a(26) = 3.
%t A229122 Table[m = 2 n - 1; NestWhile[# + 1 &, 1, !OddQ[DigitCount[m = # / 2^IntegerExponent[#, 2] & [3 m + 1], 2][[1]]] &], {n, 100}] (* _Peter J. C. Moses_, Oct 13 2013 *)
%Y A229122 Cf, A226686, A226687.
%K A229122 nonn
%O A229122 1,2
%A A229122 _Vladimir Shevelev_, Oct 07 2013
%E A229122 More terms from _Peter J. C. Moses_