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Sum of factorial of digits is prime.
6

%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