A210767 -id:A210767 - cp's OEIS frontend

A359449 Positive integers in which the sum of the k-th powers of their digits is a prime number for k = 1, 2, 3, 4, 5, and 6 but not for k=7.

223, 232, 322, 1349, 1394, 1439, 1493, 1934, 1943, 2023, 2032, 2203, 2230, 2302, 2320, 3022, 3149, 3194, 3202, 3220, 3419, 3491, 3914, 3941, 4139, 4193, 4319, 4391, 4913, 4931, 9134, 9143, 9314, 9341, 9413, 9431, 10349, 10394, 10439, 10493, 10934, 10943, 13049, 13094, 13409, 13490, 13904, 13940

Offset: 1

José Hernández, Jan 02 2023

			223 belongs to this sequence because 2+2+3=7, 2^2+2^2+3^2=17, 2^3+2^3+3^3=43, 2^4+2^4+3^4=113, 2^5+2^5+3^5=307, and 2^6+2^6+3^6=857 are prime numbers whereas 2^7+2^7+3^7 is a composite number.

Cf. A028834, A108662, A225534, A210767, A245358.

filter:= proc(n) local L,t,k;
  L:= convert(n,base,10);
  andmap(isprime, [seq(add(t^k,t=L),k=1..6)]) and not isprime(add(t^7,t=L))
end proc:
select(filter, [$1..20000]); # Robert Israel, Jan 03 2023

For[a = 0, a <= 9, a++,
 For[b = 0, b <= 9, b++,
 For[c = 0, c <= 9, c++,
 For[d = 0, d <= 9, d++,
   If[PrimeQ[a + b + c + d] == True &&
      PrimeQ[a^2 + b^2 + c^2 + d^2] == True &&
      PrimeQ[a^3 + b^3 + c^3 + d^3] == True &&
      PrimeQ[a^4 + b^4 + c^4 + d^4] == True &&
      PrimeQ[a^5 + b^5 + c^5 + d^5] == True &&
      PrimeQ[a^6 + b^6 + c^6 + d^6] == True &&
      PrimeQ[a^7 + b^7 + c^7 + d^7] == False, Print[a, b, c, d]]]]]]
(* This code outputs all the terms of the sequence in the interval [1,10^4]. *)

isok(n) = my(d=digits(n)); for (i=1, 6, if (!isprime(sum(k=1,#d, d[k]^i)), return(0))); !isprime(sum(k=1,#d, d[k]^7)); \\ Michel Marcus, Jan 02 2023

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

Original entry on oeis.org

11, 101, 110, 111, 119, 128, 133, 182, 188, 191, 218, 223, 227, 229, 232, 247, 272, 274, 281, 292, 313, 322, 331, 337, 346, 359, 364, 368, 373, 377, 379, 386, 395, 397, 427, 436, 463, 472, 478, 487, 539, 557, 568, 575, 577, 586, 593, 634, 638, 643, 658, 667

Offset: 1

José Hernández, Jan 06 2023

It is easy to establish that the sequence is infinite: if x is in the sequence, so is 10*x.

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

			11 is a term since 1^5 + 1^5 = 2 is prime.

A031974 is a subsequence.
Cf. A055014 (sum of the 5th powers of digits).
Cf. A028834, A108662, A225534, A210767, A245358.

top = 999; (* Find all terms <= top *)
For[t = 11, t <= top, t++, k = IntegerLength[t]; sum = 0;
   For[e = 0, e <= k - 1, e++, sum = sum + NumberDigit[t, e]^5];
      If[PrimeQ[sum] == True, Print[t]]]
Select[Range[670],PrimeQ[Total[IntegerDigits[#]^5]] &] (* Stefano Spezia, Jan 08 2023 *)

isok(k) = isprime(vecsum(apply(x->x^5, digits(k)))); \\ Michel Marcus, Jan 07 2023

cp's OEIS Frontend

A359449 Positive integers in which the sum of the k-th powers of their digits is a prime number for k = 1, 2, 3, 4, 5, and 6 but not for k=7.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

PARI