A257680 Characteristic function for A256450: 1 if there is at least one 1-digit present in the factorial representation of n (A007623), otherwise 0.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

Formula

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.]

Mathematica

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 *)

Prog

(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:
(definec (A257680 n) (cond ((zero? n) 0) ((= 1 (A099563 n)) 1) (else (A257680 (A257687 n)))))
(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
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Characteristic function of A256450.

Cf. A255411 (gives the positions of zeros), A257682 (partial sums).

Cf. also A007623, A099563, A257685, A257687.

Sequence in context: A351039 A022930 A285596 * A323377 A068344 A161382

Adjacent sequences: A257677 A257678 A257679 * A257681 A257682 A257683

Keyword

nonn,base

Author

Antti Karttunen, May 04 2015

Status

approved