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A084405 Primes whose sum of factorials of digits is also prime.

%I A084405 #15 Feb 11 2023 20:34:30
%S A084405 2,11,13,31,101,163,313,331,431,503,613,631,1021,1201,1223,1433,1439,
%T A084405 1453,1483,1493,1543,1567,1657,1663,1667,1669,1753,1777,1789,1879,
%U A084405 1987,1999,2011,2111,2203,2213,2221,3049,3163,3221,3313,3331,3361,3413,3461,3491
%N A084405 Primes whose sum of factorials of digits is also prime.
%H A084405 Harvey P. Dale, <a href="/A084405/b084405.txt">Table of n, a(n) for n = 1..1000</a>
%e A084405 a(10)=503, a prime, and 5! + 0! + 3! = 127, a prime.
%t A084405 Select[Prime[Range[500]],PrimeQ[Total[IntegerDigits[#]!]]&] (* _Harvey P. Dale_, Mar 20 2016 *)
%o A084405 (PARI) {digitsumfac(n)=local(s, d); s=0; while(n>0,d=divrem(n,10); n=d[1]; s=s+d[2]!); s}
%o A084405 {facp(m)=local(ct,sr); ct=0; sr=0; forprime(p=2,m, if(isprime(digitsumfac(p)),ct++; print1(p," "); sr+=(1.0/p); )); print(); print("Found: "ct" primes < "m); print("Sum of reciprocals = "sr); }
%o A084405 (Python)
%o A084405 from sympy import isprime
%o A084405 from math import factorial
%o A084405 def f(n): return sum(factorial(int(d)) for d in str(n))
%o A084405 def ok(n): return isprime(n) and isprime(f(n))
%o A084405 print([k for k in range(3500) if ok(k)]) # _Michael S. Branicky_, Feb 11 2023
%Y A084405 Cf. A061602.
%K A084405 base,easy,nonn
%O A084405 1,1
%A A084405 _Jason Earls_, Jun 24 2003