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

1,2

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

Links

Table of n, a(n) for n=1..83.

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

Crossrefs

Cf. A055945.

Sequence in context: A235431 A354599 A303536 * A096370 A330721 A076622

Adjacent sequences: A259653 A259654 A259655 * A259657 A259658 A259659

Keyword

nonn,base

Author

Dylan Hamilton, Jul 02 2015

Status

approved