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 A084405 Primes whose sum of factorials of digits is also prime. 2
 2, 11, 13, 31, 101, 163, 313, 331, 431, 503, 613, 631, 1021, 1201, 1223, 1433, 1439, 1453, 1483, 1493, 1543, 1567, 1657, 1663, 1667, 1669, 1753, 1777, 1789, 1879, 1987, 1999, 2011, 2111, 2203, 2213, 2221, 3049, 3163, 3221, 3313, 3331, 3361, 3413, 3461, 3491 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE a(10)=503, a prime, and 5! + 0! + 3! = 127, a prime. MATHEMATICA Select[Prime[Range[500]], PrimeQ[Total[IntegerDigits[#]!]]&] (* Harvey P. Dale, Mar 20 2016 *) PROG (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); } (Python) from sympy import isprime from math import factorial def f(n): return sum(factorial(int(d)) for d in str(n)) def ok(n): return isprime(n) and isprime(f(n)) print([k for k in range(3500) if ok(k)]) # Michael S. Branicky, Feb 11 2023 CROSSREFS Cf. A061602. Sequence in context: A075781 A023288 A106960 * A041447 A291464 A262832 Adjacent sequences: A084402 A084403 A084404 * A084406 A084407 A084408 KEYWORD base,easy,nonn AUTHOR Jason Earls, Jun 24 2003 STATUS approved

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