A257680 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

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).