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

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, 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, 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

Offset

1,2

Comments

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.

References

R. K. Guy, Unsolved Problems in Number Theory, B6.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..275

Prog

(Scheme)
(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)))))))
(define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
;; Antti Karttunen, Nov 02 2017

Crossrefs

Cf. A098008, A098007, A044050, A003023.

Sequence in context: A217721 A071862 A030362 * A044050 A096826 A346010

Adjacent sequences: A007903 A007904 A007905 * A007907 A007908 A007909

Keyword

sign

Author

Michael Gerenrot (sch116(AT)yahoo.com)

Extensions

Definition changed by N. J. A. Sloane, Nov 02 2017 at the suggestion of Antti Karttunen.

Status

approved