

A276004


a(n) = number of nonzero digits in factorial base representation of n that are hit by more significant digits from left; a(n) = A060502(n)  A060128(n).


6



0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 3, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 0, 1, 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 position i of factorial base representation of n (where the least significant digit is in the position 1) such that there is another nonzero digit d_j in such position j > i that j  d_j = i.


LINKS

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


FORMULA

a(n) = A060502(n)  A060128(n).
a(n) = A000120(2*A275727(n) AND A276010(n)), where AND is a bitwiseand given in A004198.


EXAMPLE

For n=15 ("211" in factorial base) the least significant 1 at position 1 is hit by its immediate left neighbor 1 and also by 2 at position 3, as (21) = (32) = 1, the position where the least significant 1 itself is. However, this is counted just as one hit, because this sequence gives the number of digits that are hit, instead of number digits that hit, thus a(15)=1.


PROG

(Scheme, two variants)
(define (A276004 n) ( (A060502 n) (A060128 n)))
(define (A276004 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))) (cond ((zero? d) (loop (+ 1 i) c)) ((zero? (vectorref fv ( i d))) (loop (+ 1 i) c)) (else (begin (vectorset! fv ( i d) 0) (loop (+ 1 i) (+ 1 c))))))))))
(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. A000120, A004198, A060128, A060502, A275727, A276010.
Cf. A276005 (indices of zeros), A276006 (of nonzeros).
Differs from A276007 for the first time at n=15, where a(15)=1, while A276004(15)=2.
Sequence in context: A287156 A092510 A117208 * A133300 A178779 A144451
Adjacent sequences: A276001 A276002 A276003 * A276005 A276006 A276007


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 17 2016


STATUS

approved



