cp's OEIS Frontend

A359610 Numbers k such that the sum of the 5th powers of the digits of k is prime.

%I A359610 #28 Jan 28 2023 03:55:31
%S A359610 11,101,110,111,119,128,133,182,188,191,218,223,227,229,232,247,272,
%T A359610 274,281,292,313,322,331,337,346,359,364,368,373,377,379,386,395,397,
%U A359610 427,436,463,472,478,487,539,557,568,575,577,586,593,634,638,643,658,667
%N A359610 Numbers k such that the sum of the 5th powers of the digits of k is prime.
%C A359610 It is easy to establish that the sequence is infinite: if x is in the sequence, so is 10*x.
%C A359610 Alternatively: the sequence is infinite as the sequence contains all numbers consisting of a prime number of 1s and an arbitrary number of 0s. - _Charles R Greathouse IV_, Jan 06 2023
%e A359610 11 is a term since 1^5 + 1^5 = 2 is prime.
%t A359610 top = 999; (* Find all terms <= top *)
%t A359610 For[t = 11, t <= top, t++, k = IntegerLength[t]; sum = 0;
%t A359610    For[e = 0, e <= k - 1, e++, sum = sum + NumberDigit[t, e]^5];
%t A359610       If[PrimeQ[sum] == True, Print[t]]]
%t A359610 Select[Range[670],PrimeQ[Total[IntegerDigits[#]^5]] &] (* _Stefano Spezia_, Jan 08 2023 *)
%o A359610 (PARI) isok(k) = isprime(vecsum(apply(x->x^5, digits(k)))); \\ _Michel Marcus_, Jan 07 2023
%Y A359610 A031974 is a subsequence.
%Y A359610 Cf. A055014 (sum of the 5th powers of digits).
%Y A359610 Cf. A028834, A108662, A225534, A210767, A245358.
%K A359610 nonn,base,easy
%O A359610 1,1
%A A359610 _José Hernández_, Jan 06 2023