

A179480


Let m>k>0 be odd numbers and denote by the symbol "m<>k" the value A000265(mk). 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*n1, 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
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OFFSET

2,3


COMMENTS

A dual sequence to A179382
Let b = (2*n1) and k = A003558(n1). 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 (n1)/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(xop(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*n1, 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



