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 A084405 Primes such that the sum of the factorials of the digits is also prime. 1

%I

%S 2,11,13,31,101,163,313,331,431,503,613,631,1021,1201,1223,1433,1439,

%T 1453,1483,1493,1543,1567,1657,1663,1667,1669,1753,1777,1789,1879,

%U 1987,1999,2011,2111,2203,2213,2221,3049,3163,3221,3313,3331,3361,3413,3461

%N Primes such that the sum of the factorials of the digits is also prime.

%H Harvey P. Dale, <a href="/A084405/b084405.txt">Table of n, a(n) for n = 1..1000</a>

%e a(10)=503, a prime and 5!+0!+3!= 127, a prime.

%t Select[Prime[Range[500]],PrimeQ[Total[IntegerDigits[#]!]]&] (* _Harvey P. Dale_, Mar 20 2016 *)

%o (PARI) {digitsumfac(n)=local(s, d); s=0; while(n>0,d=divrem(n,10); n=d[1]; s=s+d[2]!); s} {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); }

%Y Cf. A061602.

%K base,easy,nonn

%O 1,1

%A _Jason Earls_, Jun 24 2003

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)