|
%I #24 Jun 02 2021 04:20:58
%S 2,3,7,11,13,29,37,241,1429,2437,2741,4583,7333,8269,36073,37397,
%T 48121,73037,130261,147289,280037,1032259,6594787,10249573,130193849,
%U 443038781,527454197,1024907927,1736090963,2602512709,13517865841,13684220029,64209198247,93380481511,126718347859,143176188581,231059158871,273286859737,511940464493,512760363097,715173864563,810985955573
%N Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^19) / k is an integer.
%C a(51) > 491952295618219. - _Bruce Garner_, Jun 02 2021
%H Bruce Garner, <a href="/A233769/b233769.txt">Table of n, a(n) for n = 1..50</a> (first 42 terms from Robert Price)
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e 13 is a term, because 13 is the 6th prime and the sum of the first 6 primes^19+1 = 1523090798793695143992 when divided by 6 equals 253848466465615857332 which is an integer.
%t t = {}; sm = 1; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^19); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn
%O 1,1
%A _Robert Price_, Dec 15 2013
|
