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.

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, 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, 1, 2, 3, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2

Offset: 1

Author

Vladimir Shevelev, Oct 07 2013

Keywords

• nonn

Comments

Since 1 is odious number, the conjecture that all a(n) > 0 is a very weak form of the "3x+1" (Collatz) conjecture.

We conjecture that this sequence is unbounded.

Examples

			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.
		

Crossrefs

Cf, A226686, A226687.

Programs

Mathematica

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 *)

Extensions

More terms from Peter J. C. Moses