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

0,10

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Index entries for sequences related to factorial base representation

Example

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.

Prog

(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))))))

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.

Sequence in context: A328194 A131963 A130538 * A351619 A078659 A374080

Adjacent sequences: A276004 A276005 A276006 * A276008 A276009 A276010

Keyword

nonn,base

Author

Antti Karttunen, Aug 17 2016

Status

approved