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A257680
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Characteristic function for A256450: 1 if there is at least one 1-digit present in the factorial representation of n (A007623), otherwise 0.
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19
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0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0
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LINKS
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FORMULA
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a(0) = 0; for n >= 1, if A099563(n) = 1, then a(n) = 1, otherwise a(n) = a(A257687(n)).
Other identities:
a(2n+1) = 1 for all n. [Because all odd numbers end with digit 1 in factorial base.]
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MATHEMATICA
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a[n_] := Module[{k = n, m = 2, c = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r == 1, c++]; m++]; If[c > 0, 1, 0]]; Array[a, 100, 0] (* Amiram Eldar, Jan 23 2024 *)
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PROG
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(Scheme)
(define (A257680 n) (let loop ((n n) (i 2)) (cond ((zero? n) 0) ((= 1 (modulo n i)) 1) (else (loop (floor->exact (/ n i)) (+ 1 i))))))
;; As a recurrence utilizing memoizing definec-macro:
(Python)
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a(n): return 1 if '1' in str(a007623(n)) else 0
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CROSSREFS
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Characteristic function of A256450.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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