

A203640


Length of the cycle reached for the map x>A203639(x), starting at n.


3



1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET

1,16


COMMENTS

Differs from A063775 at n = 64, 81, 128, 144, 162, 192, ... Differs from A053164 at n = 64, 81, 128, 144, 162, 192, 216, 243,... Differs from A043289 at n = 64, 128, 144, 192, 216, 225,...  R. J. Mathar, Jan 11 2012


LINKS



EXAMPLE

Starting from n = 12, the derived sequence is A203639(12) = 4, A203639(4) = 4, A203639(4) = 4, etc, and the sequence 12, 4, 4, 4, 4, ... has cycle length 1. Therefore a(12) = 1.
Starting from n = 16, the derived sequence is A203639(16) = 32, A203639(32) = 80, A203639(80) = 32, etc, and the sequence 16, 32, 80, 32, 80, ... has cycle length 2. Therefore a(16) = 2.
Starting from n = 2916, the derived sequence is A203639(2916) = 5832, A203639(5832) = 17496, A203639(17496) = 61236, A203639(61236) = 20412, A203639(20412) = 5832, etc, and the sequence 2916, 5832, 17496, 61236, 20412, 5832, 17496, 61236, 20412, ... has cycle length 4. Therefore a(2916) = 4. This is also the first point where the sequence attains a value larger than 2. (End)


MAPLE

idx := proc(L, n) for i from 1 to nops(L) do if op(i, L)=n then return i ; end if; end do: return 1; end proc:
A203640 := proc(n) local s, dr, d; s := [n] ; dr :=n ; for d from 1 do dr := A203639(dr) ; ii := idx(s, dr) ; if ii >0 then return nops(s)ii+1 ; else s := [op(s), dr] ; end if ; end do: end proc:


PROG

(Scheme)
(define (A203640 n) (let loop ((visited (list n)) (i 1)) (let ((next (A203639 (car visited)))) (cond ((member next visited) => (lambda (prepath) (+ 1 ( i (length prepath))))) (else (loop (cons next visited) (+ 1 i)))))))


CROSSREFS



KEYWORD

nonn,less


AUTHOR



STATUS

approved



