A203640 - OEIS

%I #22 Sep 14 2017 09:30:24

%S 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,

%T 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,

%U 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1

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

%C 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

%H Antti Karttunen, <a href="/A203640/b203640.txt">Table of n, a(n) for n = 1..65537</a>

%e 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.

%e From _Antti Karttunen_, Sep 13 2017: (Start)

%e 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.

%e 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)

%p 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:

%p 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:

%o (Scheme)

%o (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)))))))

%o ;; (Code for A203639 given under that entry.) - _Antti Karttunen_, Sep 13 2017

%K nonn,less

%O 1,16

%A _R. J. Mathar_, Jan 04 2012