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%I #36 Oct 18 2023 10:06:26
%S 2,3,5,7,11,12,14,16,21,23,25,27,32,38,41,45,49,52,54,56,58,61,65,72,
%T 78,83,85,87,94,101,110,111,113,115,122,124,128,131,139,142,146,148,
%U 151,155,164,166,182,184,193,199,212,214,218,221,223,227,232,236,238,241
%N Positive integers whose digit-power sum is a prime.
%C 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.
%C Numbers k such that A101337(k) is prime.
%C 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.
%H Robert Israel, <a href="/A330125/b330125.txt">Table of n, a(n) for n = 1..10000</a>
%H Math Misery, <a href="http://mathmisery.com/wp/2019/12/01/of-probes-and-primes/">Of Probes and Primes</a>
%e The first four terms are the single-digit primes; a(5) = 11 since 1^2 + 1^2 = 2, which is prime.
%p filter:= proc(n) local L,d,t;
%p L:= convert(n,base,10);
%p d:= nops(L);
%p isprime(add(t^d, t=L))
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, Oct 17 2023
%t Select[Range[250], (d = IntegerDigits[#]; PrimeQ@ Total[d^Length[d]]) &] (* _Giovanni Resta_, Dec 02 2019 *)
%o (PARI) isok(n) = {my(d = digits(n)); isprime(sum(k=1, #d, d[k]^#d));} \\ _Michel Marcus_, Dec 05 2019
%Y Cf. A101337, A139749, A178357.
%K nonn,base,easy
%O 1,1
%A _Manan Shah_, Dec 01 2019
%E More terms from _Giovanni Resta_, Dec 02 2019
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