A339928 Numbers k such that the removal of all terminating even digits from k! leaves a prime.

6, 7, 9, 10, 43, 138, 1068

Offset: 1

Author

Derek Orr, Dec 23 2020

Keywords

• nonn
• base
• more

Comments

a(8) > 1500.

If only the terminating zeros are removed, 2 is the only number whose factorial becomes prime.

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.

a(8) > 20000. - Michael S. Branicky, Jul 05 2024

Examples

			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.
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.
		

Crossrefs

Cf. A000142.

Programs

PARI

for(n=1,1500,k=n!;while(!(k%2),k\=10;if(k==0,break));if(isprime(k),print1(n,", ")))

Python

from sympy import factorial, isprime
def ok(n):
    fn = factorial(n)
    while fn > 0 and fn%2 == 0: fn //= 10
    return fn > 0 and isprime(fn)
print(list(filter(ok, range(200)))) # Michael S. Branicky, Jun 07 2021