A179480 Let m>k>0 be odd numbers and denote by the symbol "m<->k" the value A000265(m-k). Then the sequence m<->k, m<->(m<->k), m<->(m<->(m<->k)), ... is periodic; a(n) is the smallest period in the case m=2*n-1, k=1.

1, 1, 2, 1, 3, 3, 2, 1, 5, 2, 6, 5, 5, 7, 2, 1, 6, 9, 6, 3, 3, 6, 12, 10, 4, 13, 10, 3, 15, 15, 2, 1, 17, 10, 18, 2, 10, 14, 20, 13, 21, 2, 14, 4, 6, 4, 18, 11, 9, 25, 26, 4, 27, 9, 18, 5, 22, 4, 12, 27, 10, 25, 2, 1, 33, 6, 18, 15, 35, 22, 30, 3, 22, 37, 6, 12, 10, 13, 26

Offset: 2

Author

Vladimir Shevelev, Jul 16 2010

Keywords

• nonn

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.

Iff a(n) = n/2 or (n-1)/2, then 2*n - 1 is a prime with one coach and is in A216371. Examples: a(19) = 9, so 37 is in A216371. a(12) = 6, so 23 is in A216371. - _Gary W. Adamson, Sep 08 2012.

Examples

			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.
		

Crossrefs

Cf. A179382, A179383, A000265.

Cf. A003558.

Cf. A216371.

Programs

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:
A179480 := proc(n) A179480aux(2*n-1,1) ; end proc: seq(A179480(n),n=2..80) ; (End)

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 *)

Extensions

Edited by N. J. A. Sloane, Jul 18 2010

More terms from R. J. Mathar, Nov 04 2010