2,3

A dual sequence toA179382.

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 andA003558(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 inA216371.Examples: a(19) = 9, so 37 is inA216371.a(12) = 6, so 23 is inA216371.- _Gary W. Adamson, Sep 08 2012.

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.

Contribution fromR. 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)

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, afterR. J. Mathar*)

Cf.A179382,A179383,A000265.

Cf.A003558.

Cf.A216371.

Sequence in context:A262209A324338A047679*A245326A241534A337137

Adjacent sequences:A179477A179478A179479*A179481A179482A179483

Vladimir Shevelev,Jul 16 2010

Edited byN. J. A. Sloane,Jul 18 2010

More terms fromR. J. Mathar,Nov 04 2010

approved