A230406 a(n) = A034968(A219666(n)); after zero, the differences between successive nodes in the infinite trunk of the factorial beanstalk (A219666).

0, 1, 1, 3, 2, 3, 2, 5, 6, 2, 3, 2, 5, 5, 6, 2, 4, 5, 6, 7, 4, 5, 6, 7, 5, 5, 7, 10, 2, 3, 2, 5, 5, 6, 2, 4, 5, 6, 7, 4, 5, 6, 7, 5, 5, 6, 9, 8, 7, 10, 2, 4, 5, 6, 7, 4, 5, 6, 7, 5, 5, 6, 8, 6, 8, 8, 7, 10, 11, 4, 5, 6, 7, 5, 5, 6, 8, 6, 8, 8, 7, 10, 12, 10, 11

Offset: 0

Author

Antti Karttunen, Nov 09 2013

Keywords

• nonn

Comments

Also the first differences of A219666, shifted once right and prepended with zero.

This sequence relates to the factorial base representation (A007623) in the same way as A213712 relates to the binary system.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..3149

Crossrefs

Cf. also A230418, A230410.

Programs

Scheme

(define (A230406 n) (A034968 (A219666 n)))
;; Alternative definition:
(define (A230406 n) (if (zero? n) n (- (A219666 n) (A219666 (- n 1)))))

Formula

a(n) = A034968(A219666(n)).

a(0) = 0, and for n>=1, a(n) = A219666(n) - A219666(n-1).

a(A226061(n)) = A000217(n-1) for all n.