A232865 Primes p such that the average of the seventh power of primes up to p is an integer.

2, 97, 14293, 247997, 7979737, 15749303, 344468591, 25934255929, 40224745543, 16495569405383, 53941465463489, 84897825837611, 244949151647509, 757938163218799, 1594375071689591, 1674528348898463, 5347819657753523, 6152744788157173, 47008163075851819

Offset

1,1

Comments

Otherwise said, prime(m) such that m divides prime(1)^7 + ... + prime(m)^7.

a(17) > 1877564517734839. - Bruce Garner, Aug 30 2021

a(18) > 5493145969370039. - Paul W. Dyson, Mar 02 2022

a(19) > 6728882502496787. - Bruce Garner, Sep 18 2022

Links

Table of n, a(n) for n=1..19.

OEIS Wiki, Sums of powers of primes divisibility sequences

Formula

a(n) = prime(A125826(n)).

Prog

(PARI) S=n=0; forprime(p=1, , (S+=p^7)%n++||print1(p", "))

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A223936 A224083 A285023 * A173837 A351447 A036901

Adjacent sequences: A232862 A232863 A232864 * A232866 A232867 A232868

Keyword

nonn,more,hard

Author

M. F. Hasler, Dec 01 2013

Extensions

a(10) from Paul W. Dyson, Jan 05 2021

a(11)-a(12) from Bruce Garner, Feb 26 2021

a(13) from Bruce Garner, Mar 23 2021

a(14) from Bruce Garner, May 19 2021

a(15)-a(16) from Bruce Garner, Aug 30 2021

a(17) from Paul W. Dyson, Mar 02 2022

a(18) from Bruce Garner, Sep 18 2022

a(19) from Paul W. Dyson, Jan 17 2024

Status

approved