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%I #9 Feb 23 2023 11:53:30
%S 2,10,11,12,13,20,21,30,31,100,101,110,111,122,133,134,135,136,143,
%T 153,155,163,178,187,202,212,220,221,303,304,305,306,313,314,315,316,
%U 330,331,340,341,350,351,360,361,403,413,430,431,503,505,513,515,530,531
%N Sum of factorial of digits is prime.
%e 1!+3!+5! = 127 and 127 is prime, so 135 appears in the sequence.
%o (PARI) digfac(n)=local(s=0); while(n,s=s+((n%10)!);n=n\10);return(s)
%o for(n=1,1000,if(isprime(digfac(n)),print1(n,", ")))
%o (Python)
%o from itertools import count, islice, combinations_with_replacement
%o from math import factorial
%o from sympy import isprime
%o from sympy.utilities.iterables import multiset_permutations
%o def A165451_gen(): # generator of terms
%o for l in count(0):
%o for i in range(1,10):
%o fi = factorial(i)
%o 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))))
%o A165451_list = list(islice(A165451_gen(),50)) # _Chai Wah Wu_, Feb 23 2023
%Y Cf. A061602.
%K easy,nonn,base
%O 1,1
%A _Rémy Sigrist_, Sep 20 2009
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