A203640 Length of the cycle reached for the map x->A203639(x), starting at n.

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

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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.
From Antti Karttunen, Sep 13 2017: (Start)
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)))))))
;; (Code for A203639 given under that entry.) - Antti Karttunen, Sep 13 2017

Crossrefs

Sequence in context: A043290 A356153 A194333 * A043289 A063775 A053164

Adjacent sequences: A203637 A203638 A203639 * A203641 A203642 A203643

Keyword

nonn,less

Author

R. J. Mathar, Jan 04 2012

Status

approved