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

1,2

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.

Links

Table of n, a(n) for n=1..87.

Example

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.

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 *)

Crossrefs

Cf, A226686, A226687.

Sequence in context: A029364 A122586 A079487 * A069010 A353332 A353362

Adjacent sequences: A229119 A229120 A229121 * A229123 A229124 A229125

Keyword

nonn

Author

Vladimir Shevelev, Oct 07 2013

Extensions

More terms from Peter J. C. Moses

Status

approved