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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

Table of n, a(n) for n=2..80.

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)

CROSSREFS

Cf. A179382, A179383, A000265

Cf. A003558

Cf. A216371

Sequence in context: A088074 A071463 A047679 * A245326 A241534 A035050

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 August 21 00:33 EDT 2014. Contains 245826 sequences.