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.
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Oct 07 2013
EXTENSIONS
More terms from Peter J. C. Moses
STATUS
approved