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A007906 Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.

%I A007906 #14 Nov 02 2017 15:34:53
%S A007906 1,2,2,3,2,-1,2,3,4,4,2,7,2,5,5,6,2,4,2,7,3,6,2,5,-1,7,3,-1,2,15,2,3,
%T A007906 6,8,3,4,2,7,3,4,2,14,2,5,7,8,2,6,4,3,4,9,2,13,3,5,3,4,2,11,2,9,3,4,3,
%U A007906 12,2,5,4,6,2,9,2,5,5,5,3,11,2,7,5,6,2,6,3,9,7,7,2,10,4,6,4,4,-1,9,2,3
%N A007906 Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.
%C A007906 Length of transient part of trajectory of n if trajectory reaches 1, otherwise a(n) = -1. See A098008 for another version. See A098007 for further information.
%D A007906 R. K. Guy, Unsolved Problems in Number Theory, B6.
%D A007906 R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.
%H A007906 Antti Karttunen, <a href="/A007906/b007906.txt">Table of n, a(n) for n = 1..275</a>
%o A007906 (Scheme)
%o A007906 (define (A007906 n) (let loop ((visited (list n)) (i 1)) (let ((next (A001065 (car visited)))) (cond ((zero? next) i) ((member next visited) -1) (else (loop (cons next visited) (+ 1 i)))))))
%o A007906 (define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
%o A007906 ;; _Antti Karttunen_, Nov 02 2017
%Y A007906 Cf. A098008, A098007, A044050, A003023.
%K A007906 sign
%O A007906 1,2
%A A007906 Michael Gerenrot (sch116(AT)yahoo.com)
%E A007906 Definition changed by _N. J. A. Sloane_, Nov 02 2017 at the suggestion of _Antti Karttunen_.