A379944 - OEIS

%I #30 Jan 17 2025 03:38:36

%S 0,0,1,0,1,0,1,1,0,1,1,1,2,0,0,2,1,1,0,7,1,1,2,1,0,5,0,0,1,8,1,0,1,6,

%T 1,3,1,2,1,1,0,1,8,38,1,2,1,1,5,34,1,5,6,0,1,0,1,6,1,2,2,1,1,2,8,9,1,

%U 1,1,2,2,0,2,5,1,1,0,4,2,2,1,1,2,1,1,1,1

%N Smallest number of leading digits of n! that form a prime (or 0 if none exist).

%C It appears that as n gets large, a(n) can become arbitrarily large.

%C It appears that values of n such that a(n) = 0 exist for arbitrarily large n.

%H Carson R. Smith, <a href="/A379944/b379944.txt">Table of n, a(n) for n = 0..2000</a>

%e For n = 3, 3! = 6, 6 is not prime, a(3) = 0.

%e For n = 19, 19! = 121645100408832000, 1216451 is the smallest prime, a(19) = 7.

%t A379944[n_] := Catch[Do[If[PrimeQ[FromDigits[#[[;; k]]]], Throw[k]],{k,Length[#]}] & [IntegerDigits[n!]]; 0];

%t Array[A379944, 100, 0] (* _Paolo Xausa_, Jan 16 2025 *)

%o (Python)

%o import math

%o from sympy import isprime

%o def a(n):

%o     factorial = str(math.factorial(n))

%o     for d in range(1, len(factorial)+1):

%o         if isprime(int(factorial[:d])):

%o             return d

%o     return 0

%o (PARI) a(n) = my(d=digits(n!)); for (k=1, #d, if (isprime(fromdigits(Vec(d, k))), return(k))); \\ _Michel Marcus_, Jan 08 2025

%Y Cf. A000040, A000142, A046277.

%K nonn,base

%O 0,13

%A _Carson R. Smith_, Jan 07 2025

%E More terms from _Jinyuan Wang_, Jan 07 2025