A165451 Sum of factorial of digits is prime.

2, 10, 11, 12, 13, 20, 21, 30, 31, 100, 101, 110, 111, 122, 133, 134, 135, 136, 143, 153, 155, 163, 178, 187, 202, 212, 220, 221, 303, 304, 305, 306, 313, 314, 315, 316, 330, 331, 340, 341, 350, 351, 360, 361, 403, 413, 430, 431, 503, 505, 513, 515, 530, 531

Offset: 1

Author

Rémy Sigrist, Sep 20 2009

Keywords

• easy
• nonn
• base

Examples

			1!+3!+5! = 127 and 127 is prime, so 135 appears in the sequence.
		

Crossrefs

Cf. A061602.

Programs

PARI

digfac(n)=local(s=0); while(n,s=s+((n%10)!);n=n\10);return(s)
for(n=1,1000,if(isprime(digfac(n)),print1(n,", ")))

Python

from itertools import count, islice, combinations_with_replacement
from math import factorial
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A165451_gen(): # generator of terms
    for l in count(0):
        for i in range(1,10):
            fi = factorial(i)
            yield from sorted(int(str(i)+''.join(map(str,k))) for j in combinations_with_replacement(range(10), l) for k in multiset_permutations(j) if isprime(fi+sum(map(factorial,j))))
A165451_list = list(islice(A165451_gen(),50)) # Chai Wah Wu, Feb 23 2023