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

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

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