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 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. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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. 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. LINKS 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: 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 *) CROSSREFS Cf. A179382, A179383, A000265 Cf. A003558 Cf. A216371 Sequence in context: A262209 A324338 A047679 * A245326 A241534 A337137 Adjacent sequences:  A179477 A179478 A179479 * A179481 A179482 A179483 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

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Last modified April 13 22:18 EDT 2021. Contains 342941 sequences. (Running on oeis4.)