login
A233577
Prime(k), where k is such that (1+Sum_{i=1..k} prime(i)^18) / k is an integer.
1
2, 3, 5, 7, 13, 17, 19, 23, 37, 43, 61, 67, 73, 89, 103, 107, 151, 163, 179, 181, 197, 223, 251, 263, 269, 307, 347, 359, 373, 383, 433, 491, 587, 593, 613, 619, 701, 751, 761, 881, 997, 1019, 1129, 1321, 1439, 1601, 1699, 1951, 2069, 2243, 2267, 2297, 2423
OFFSET
1,1
COMMENTS
a(681) > 491952295618219. - Bruce Garner, Jun 06 2021
LINKS
Bruce Garner, Table of n, a(n) for n = 1..680 (first 515 terms from Robert Price, terms 516..559 from Karl-Heinz Hofmann)
EXAMPLE
13 is a term because 13 is the 6th prime and the sum of the first 6 primes^18+1 = 118016956494132483318 when divided by 6 equals 19669492749022080553 which is an integer.
MATHEMATICA
t = {}; sm = 1; Do[sm = sm + Prime[n]^18; 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)^18); 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: A344621 A255203 A356445 * A233041 A049567 A293048
KEYWORD
nonn
AUTHOR
Robert Price, Dec 13 2013
STATUS
approved