A180404 Primes p such that the sum of fifth power of their digits is a prime.

11, 101, 191, 223, 227, 229, 281, 313, 331, 337, 359, 373, 379, 397, 463, 487, 557, 577, 593, 643, 683, 733, 739, 757, 773, 821, 863, 881, 911, 937, 953, 1019, 1033, 1091, 1109, 1123, 1129, 1181, 1213, 1231, 1259, 1277, 1291, 1303, 1321, 1381, 1433, 1439

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

A prime p = abcdef... (each letter being a single digit) belongs to this sequence if sum = a^5+b^5+... is a prime. - Corrected by Robert Israel, Feb 22 2026

Example

227 is a term since 2^5+2^5+7^5 = 32+32+16807 = 16871 is a prime.

Maple

filter:= proc(n) local t;
   isprime(n) and isprime(add(t^5, t=convert(n, base, 10)))
end proc:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Feb 22 2026

Mathematica

Select[Prime[Range[500]], PrimeQ[Total[IntegerDigits[#]^5]]&] (* Harvey P. Dale, May 25 2011 *)

Crossrefs

Cf. A055014, A046704, A052034, A091366, A091367.

Sequence in context: A370447 A068188 A032592 * A142317 A180406 A174884

Adjacent sequences: A180401 A180402 A180403 * A180405 A180406 A180407

Keyword

nonn,base

Author

Carmine Suriano, Sep 02 2010

Status

approved