A121819 Minimal number m such that prime(1)^n + ... + prime(m)^n is prime.

1, 2, 4, 2, 66, 26, 6, 18, 8, 126, 48, 38, 144, 696, 38, 234, 666, 60, 4, 228, 216, 212, 168, 290, 6, 702, 14, 78, 120, 614, 222, 44, 104, 66, 58, 54, 152, 260, 858, 74, 108, 164, 336, 152, 424, 60, 118, 1154, 112, 14, 1530, 14, 296, 654, 1782, 474, 444, 462, 1338, 468

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

a(1) = 1 because 2 = 2^1 is prime. a(2) = 2 because 13 = 2^2 + 3^2 is prime but 2^2 is not prime. a(3) = 4 because 503 = 2^3 + 3^3 + 5^3 + 7^3 is prime but 8 = 2^3, 35 = 2^3 + 3^3, 160 = 2^3 + 3^3 + 5^3 are not prime.

Mathematica

s={1}; Do[m=1; Until[PrimeQ[Sum[ Prime[i]^n, {i, m}] ] , m++]; AppendTo[s, m], {n, 2, 60}]; s (* James C. McMahon, Oct 22 2024 *)

Prog

(PARI) a(n)=my(m, s); forprime(p=2, , m++; if(isprime(s+=p^n), return(m))) \\ Charles R Greathouse IV, Sep 25 2016

Crossrefs

Sequence in context: A130172 A303320 A029589 * A134138 A351427 A381410

Adjacent sequences: A121816 A121817 A121818 * A121820 A121821 A121822

Keyword

nonn

Author

Alexander Adamchuk, Aug 26 2006

Extensions

Name edited by Charles R Greathouse IV, Sep 25 2016

Status

approved