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A232865
Primes p such that the average of the seventh power of primes up to p is an integer.
2
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
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).
Sequence in context: A223936 A224083 A285023 * A173837 A351447 A036901
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