A091367 Primes p such that the sum of the digits raised to the 4th power is prime.

11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 179, 191, 197, 223, 269, 311, 313, 331, 353, 379, 397, 401, 443, 461, 601, 607, 641, 661, 719, 739, 809, 883, 911, 937, 971, 1013, 1019, 1031, 1033, 1091, 1097, 1103, 1109, 1181, 1301, 1303, 1367, 1433

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(1) = 11 because 1^4 + 1^4 = 2 which is prime.
a(10) = 89 because 8^4 + 9^4 = 10657 which is prime.

Mathematica

upto=500; Select[Prime[Range[upto]], PrimeQ[Total[IntegerDigits[#]^4]]&] (* Paolo Xausa, Nov 23 2021 *)

Prog

(Python)
from sympy import isprime, primerange
def ok(p): return isprime(sum(int(d)**4 for d in str(p)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(1433)) # Michael S. Branicky, Nov 23 2021

Crossrefs

Cf. A046704 (primes whose digits sum to a prime), A052034 (primes whose digits squared sum to a prime), A091366 (primes whose digits cubed sum to a prime).

Sequence in context: A136000 A054723 A109981 * A088136 A164932 A086244

Adjacent sequences: A091364 A091365 A091366 * A091368 A091369 A091370

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004

Status

approved