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%I #21 Jun 07 2021 20:04:20
%S 6,7,9,10,43,138,1068
%N Numbers k such that the removal of all terminating even digits from k! leaves a prime.
%C a(8) > 1500.
%C If only the terminating zeros are removed, 2 is the only number whose factorial becomes prime.
%C If one also removes 5s at the end, 7 is no longer in the sequence and no numbers below 1500 are added to the sequence.
%e 43! = 60415263063373835637355132068513997507264512000000000. After removing all even digits at the end, we are left with 6041526306337383563735513206851399750726451, which is prime. So 43 is a term of this sequence.
%e 27! = 10888869450418352160768000000. After removing all even digits at the end, we are left with 108888694504183521607, which is not prime. So 27 is not a term of this sequence.
%o (PARI) for(n=1,1500,k=n!;while(!(k%2),k\=10;if(k==0,break));if(isprime(k),print1(n,", ")))
%o (Python)
%o from sympy import factorial, isprime
%o def ok(n):
%o fn = factorial(n)
%o while fn > 0 and fn%2 == 0: fn //= 10
%o return fn > 0 and isprime(fn)
%o print(list(filter(ok, range(200)))) # _Michael S. Branicky_, Jun 07 2021
%Y Cf. A000142.
%K nonn,base,more
%O 1,1
%A _Derek Orr_, Dec 23 2020
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