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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

%I

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%H Antti Karttunen, <a href="/A276007/b276007.txt">Table of n, a(n) for n = 0..40320</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%e 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.

%o (Scheme)

%o (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)))))))))

%o (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))))))

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

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

%K nonn,base

%O 0,10

%A _Antti Karttunen_, Aug 17 2016

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)