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A165451
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Sum of factorial of digits is prime.
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6
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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1!+3!+5! = 127 and 127 is prime, so 135 appears in the sequence.
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PROG
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(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))))
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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