A232869 Primes p such that the average of the fourth powers of primes up to p is an integer.

2, 26893, 741080929, 95114243761787, 146234140655742407

Offset: 1

Author

M. F. Hasler, Dec 01 2013

Keywords

• nonn
• hard
• more

Comments

Otherwise said, prime(n) such that n divides prime(1)^4 + ... + prime(n)^4. The n-values (indices) are given in A125907.

Crossrefs

Cf. A171399, A111441, A217599 (analog for squares), A223936 (3rd powers), A224083 (5th powers), A232733 (6th powers), A232865 (7th powers), A232822 (8th powers), A232962 (9th powers), A233132 (10th powers).

Programs

PARI

S=n=0;forprime(p=1,,(S+=p^4)%n++||print1(p","))

Formula

a(n) = prime(A125907(n)).

Extensions

a(4) from Bruce Garner, Feb 27 2021

a(5) from Paul W. Dyson, May 09 2024