A259656 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.

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

Offset: 1

Author

Dylan Hamilton, Jul 02 2015

Keywords

• nonn
• base

Comments

First differences appear to always be odd.

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

Crossrefs

Cf. A055945.

Programs

Maple

A259656 := proc(n)
    local f,a ;
    f := n ;
    a := 0 ;
    while f <> 0 do
        f := abs(A055945(f)) ;
        a := a+1 ;
    end do:
    a;
end proc: # R. J. Mathar, Nov 04 2015