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A232094
a(n) = A060130(A000217(n)); number of nonzero digits in factorial base representation (A007623) of 0+1+2+...+n.
5
0, 1, 2, 1, 2, 3, 3, 2, 2, 4, 3, 2, 2, 3, 4, 1, 3, 5, 4, 4, 3, 5, 3, 3, 3, 4, 5, 2, 4, 4, 5, 3, 2, 5, 4, 3, 3, 4, 4, 3, 3, 5, 6, 5, 4, 5, 3, 3, 3, 4, 5, 3, 5, 6, 5, 3, 4, 6, 5, 4, 4, 5, 6, 3, 5, 6, 4, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 4, 6, 5, 2, 6, 5, 3, 4, 4, 5
OFFSET
0,3
COMMENTS
The next 1 after a(1), a(3) and a(15) occurs at n=224, as A000217(224) = 25200 = 5 * 7!.
LINKS
FORMULA
a(n) = A060130(A000217(n)).
a(n) = A230410(A226061(n+1)). [Not a practical way to compute this sequence. Please see comments at A230410.]
MATHEMATICA
a[n_] := Module[{k = n*(n+1)/2, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; Count[s, _?(# > 0 &)]]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)
PROG
(Scheme)
(define (A232094 n) (A060130 (A000217 n)))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 18 2013
STATUS
approved