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

1,1

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

Links

Table of n, a(n) for n=1..7.

Example

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.

Prog

(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

Crossrefs

Cf. A000142.

Sequence in context: A287347 A216361 A216360 * A205877 A081053 A022892

Adjacent sequences: A339925 A339926 A339927 * A339929 A339930 A339931

Keyword

nonn,base,more

Author

Derek Orr, Dec 23 2020

Status

approved