OFFSET
2,3
COMMENTS
A dual sequence to A179382.
Let b = (2*n-1) and k = A003558(n-1). If a(n) is odd, b divides (2^k + 1); but if a(n) is even, b divides (2^k - 1). Examples: a(14) = 5, odd; with b = 27 and A003558(13) = 9. Then 27 divides (2^9 + 1) or 513 = 27 * 19. a(18) = 6, even. b = 35, with k= A003558(17) = 12. Then 35 divides (2^12 - 1). - Gary W. Adamson, Aug 20 2012.
EXAMPLE
If n=14, then m=27 and we have 27<->1=13, 27<->13=7, 27<->7=5, 27<->5=11, 27<->11=1. Thus a(14)=5.
MAPLE
Contribution from R. J. Mathar, Nov 04 2010: (Start)
A179480aux := proc(x, y) local xtrack, xitr, xpos ; xtrack := [y] ; while true do xitr := A000265(x-op(-1, xtrack)) ; if not member(xitr, xtrack, 'xpos') then xtrack := [op(xtrack), xitr] ; else return 1+nops(xtrack)-xpos ; end if; end do: end proc:
MATHEMATICA
oddres[n_] := n/2^IntegerExponent[n, 2];
b[x_, y_] := Module[{xtrack = {y}, xitr}, While[True, xitr = oddres[x - Last@ xtrack]; If[FreeQ[xtrack, xitr], AppendTo[xtrack, xitr], Return[ Length[xtrack]]]]];
a[n_] := b[2n-1, 1];
a /@ Range[2, 80] (* Jean-François Alcover, Apr 13 2020, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 16 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jul 18 2010
More terms from R. J. Mathar, Nov 04 2010
STATUS
approved