A392010 - OEIS

%I #19 Jan 29 2026 15:30:55

%S 0,0,0,0,0,3,1,1,1,1,1,2,2,1,3,2,1,1,1,7,5,3,3,10,5,6,7,11,2,2,7,10,4,

%T 10,10,11,10,10,8,10,10,9,10,10,12,10,10,10,10,11,10,13,10,10,12,11,

%U 12,10,16,10,10,10,13,17,11,10,13,12,11,10,10,13,10

%N The smallest nonnegative number k such that n! does not contain k as a substring.

%H Scott R. Shannon, <a href="/A392010/b392010.txt">Table of n, a(n) for n = 0..10000</a>

%e a(4) = 0 as 4! = 24 which does not contain '0' as a substring.

%e a(5) = 3 as 5! = 120 which does not contains '3' as a substring.

%e a(23) = 10 as 23! = 25852016738884976640000 which does not contain '10' as a substring.

%t a[n_]:=Module[{k=0}, While[SequenceCount[IntegerDigits[n!],IntegerDigits[k]]>0,k++];k];Array[a,73,0] (* _James C. McMahon_, Jan 28 2026 *)

%o (Python)

%o from gmpy2 import digits, fac

%o from itertools import count

%o def a(n):

%o     s = digits(fac(n))

%o     return next(k for k in count(0) if digits(k) not in s)

%o print([a(n) for n in range(73)]) # _Michael S. Branicky_, Jan 24 2026

%o (PARI) a(n) = my(k=0, sn=Str(n!)); while (#strsplit(sn, Str(k)) >= 2, k++); k; \\ _Michel Marcus_, Jan 24 2026

%Y Cf. A000142, A346120, A392011, A137578.

%K nonn,base

%O 0,6

%A _Scott R. Shannon_, Dec 26 2025