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A084405 Primes such that the sum of the factorials of the digits is also prime. 1
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 (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); }

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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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)