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A232824
Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^8) / k is an integer.
1
2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 47, 53, 71, 89, 107, 113, 131, 157, 167, 173, 197, 223, 281, 311, 409, 463, 503, 541, 569, 659, 751, 941, 997, 1033, 1069, 1259, 1297, 1511, 1567, 2129, 2423, 3221, 3413, 3671, 3907, 4057, 4091, 4231, 5051, 5197, 5569
OFFSET
1,1
COMMENTS
a(305) > 4193009611262897. - Bruce Garner, Mar 20 2022
LINKS
Bruce Garner, Table of n, a(n) for n = 1..304 (terms 1..227 from Robert Price)
EXAMPLE
a(5) = 11, because 11 is the 5th prime and the sum of the first 5 primes^8+1 = 220521125 when divided by 5 equals 44104225 which is an integer.
MATHEMATICA
t = {}; sm = 1; Do[sm = sm + Prime[n]^8; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
Prime[#]&/@Flatten[Position[Table[(1+Sum[Prime[n]^8, {n, k}])/k, {k, 800}], _?IntegerQ]] (* Harvey P. Dale, Aug 25 2024 *)
PROG
(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^8); s==0 \\ Charles R Greathouse IV, Nov 30 2013
CROSSREFS
Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
Sequence in context: A106639 A233462 A233893 * A078334 A108696 A215642
KEYWORD
nonn
AUTHOR
Robert Price, Nov 30 2013
STATUS
approved