

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.


5



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
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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 onebased 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 (21) = (32) = 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 (vectorlength fv)) c (let ((d (vectorref fv i))) (if (zero? d) (loop (+ 1 i) c) (loop (+ 1 i) (+ c (if (not (zero? (vectorref 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: A081400 A131963 A130538 * A078659 A079690 A257510
Adjacent sequences: A276004 A276005 A276006 * A276008 A276009 A276010


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 17 2016


STATUS

approved



