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A233194
Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^11) / k is an integer.
1
2, 3, 7, 11, 13, 29, 37, 59, 79, 197, 449, 1327, 3931, 197807, 504197, 1697743, 2595641, 6346793, 6986909, 8895379, 55664759, 63142507, 99624919, 129467011, 131784857, 239094833, 494415377, 951747371, 957443177, 9194035843, 52411358381, 62314028797, 69216548567, 220067593093, 3295153668199
OFFSET
1,1
COMMENTS
a(47) > 1005368767096627. - Bruce Garner, Jun 05 2021
EXAMPLE
13 is a term because 13 is the 6th prime and the sum of the first 6 primes^11+1 = 2079498398712 when divided by 6 equals 346583066452 which is an integer.
MATHEMATICA
t = {}; sm = 1; Do[sm = sm + Prime[n]^11; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
PROG
(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^11); 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: A233414 A233863 A371065 * A233040 A233769 A038895
KEYWORD
nonn
AUTHOR
Robert Price, Dec 05 2013
EXTENSIONS
a(35) from Karl-Heinz Hofmann, Mar 07 2021
STATUS
approved