%I #23 Nov 05 2015 12:22:13
%S 1,2,1,2,1,2,1,2,1,2,3,2,3,2,1,2,1,2,3,2,1,2,3,2,3,2,1,2,3,2,1,2,1,2,
%T 3,2,3,4,3,4,3,2,3,2,1,2,3,2,3,2,1,4,3,2,3,4,3,4,3,2,3,2,1,2,1,2,3,2,
%U 3,2,3,2,1,2,3,2,3,2,3,4,3,2,3
%N Let f(x) be the absolute value of the difference between x and its base-2 reversal. a(n) is the number of times f(x) must be applied starting with n for the result to be 0.
%C First differences appear to always be odd.
%C More precisely, a(n) is even if n is even and a(n) is odd when n is odd. This is an immediate consequence of the parities in A055945 (which represents f apart from the sign) and the fact that we count iterations of f until the result is even. - _Jörgen Backelin_, Nov 04 2015
%p A259656 := proc(n)
%p local f,a ;
%p f := n ;
%p a := 0 ;
%p while f <> 0 do
%p f := abs(A055945(f)) ;
%p a := a+1 ;
%p end do:
%p a;
%p end proc: # _R. J. Mathar_, Nov 04 2015
%Y Cf. A055945.
%K nonn,base
%O 1,2
%A _Dylan Hamilton_, Jul 02 2015