A330125 Positive integers whose digit-power sum is a prime.

2, 3, 5, 7, 11, 12, 14, 16, 21, 23, 25, 27, 32, 38, 41, 45, 49, 52, 54, 56, 58, 61, 65, 72, 78, 83, 85, 87, 94, 101, 110, 111, 113, 115, 122, 124, 128, 131, 139, 142, 146, 148, 151, 155, 164, 166, 182, 184, 193, 199, 212, 214, 218, 221, 223, 227, 232, 236, 238, 241

Offset: 1

Author

Manan Shah, Dec 01 2019

Keywords

• nonn
• base
• easy

Comments

Let M be an N-digit positive integer with digits (base 10) d_1, d_2, d_3, ..., d_N. If Sum_{i = 1..N} (d_i)^N is prime, then M is part of this sequence.

Numbers k such that A101337(k) is prime.

Both A139749 and A178357 are similar and match the first several terms of this sequence, but the digit powers are different. Additionally, perhaps a more interesting sequence is the subsequence of primes: 2, 3, 5, 7, 11, 23, 41, 61, 83.

Examples

			The first four terms are the single-digit primes; a(5) = 11 since 1^2 + 1^2 = 2, which is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Math Misery, Of Probes and Primes

Crossrefs

Cf. A101337, A139749, A178357.

Programs

Maple

filter:= proc(n) local L,d,t;
   L:= convert(n,base,10);
   d:= nops(L);
   isprime(add(t^d, t=L))
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 17 2023

Mathematica

Select[Range[250], (d = IntegerDigits[#]; PrimeQ@ Total[d^Length[d]]) &] (* Giovanni Resta, Dec 02 2019 *)

PARI

isok(n) = {my(d = digits(n)); isprime(sum(k=1, #d, d[k]^#d));} \\ Michel Marcus, Dec 05 2019

Extensions

More terms from Giovanni Resta, Dec 02 2019