A276007 a(n) = number of nonzero digits in factorial base representation of n that hit less significant nonzero digits to the right. See comments for exact definition.

0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 3, 2, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 2, 3, 2, 2, 0, 1, 1, 3, 1, 2, 0, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 3, 1, 2, 0, 2, 0, 3, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0

Offset: 0

Author

Antti Karttunen, Aug 17 2016

Keywords

• nonn
• base

Comments

a(n) = Number of times a nonzero digit d_i appears in such position i of factorial base representation of n for which there is another nonzero digit in position i - d_i. Here one-based indexing is used for digits, thus the least significant digit is in position 1.

Examples

			For n=15 ("211" in factorial base) both 2 at position 3 and 1 at position 2 hit the least significant 1 at position 1 as (2-1) = (3-2) = 1, the position where the least significant 1 itself is. These both cases are included in the count, because this sequence counts the total number of hitting digits, thus a(15)=2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..40320
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A276005 (indices of zeros), A276006 (of nonzeros).

Differs from A276004 for the first time at n=15, where a(15)=2, while A276004(15)=1.

Programs

Scheme

(define (A276007 n) (let ((fv (list->vector (cons 0 (reverse (n->factbase n)))))) (let loop ((i 1) (c 0)) (if (>= i (vector-length fv)) c (let ((d (vector-ref fv i))) (if (zero? d) (loop (+ 1 i) c) (loop (+ 1 i) (+ c (if (not (zero? (vector-ref fv (- i d)))) 1 0)))))))))
(define (n->factbase n) (let loop ((n n) (fex (if (zero? n) (list 0) (list))) (i 2)) (cond ((zero? n) fex) (else (loop (floor->exact (/ n i)) (cons (modulo n i) fex) (+ 1 i))))))