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%I #29 May 05 2021 20:56:49
%S 2,3,5,7,13,23,37,41,101,107,197,317,1033,2029,2357,2473,2879,5987,
%T 6173,35437,56369,81769,195691,199457,793187,850027,1062931,1840453,
%U 2998421,4217771,6200923,9914351,10153807,13563889,18878099,60767923,118825361,170244929
%N Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^2) / k is an integer.
%C a(51) > 1428199016921.
%C a(67) > 2407033812270611. - _Bruce Garner_, May 05 2021
%H Bruce Garner, <a href="/A233862/b233862.txt">Table of n, a(n) for n = 1..66</a> (first 50 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 a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^2+1 = 378 when divided by 6 equals 63 which is an integer.
%t t = {}; sm = 1; Do[sm = sm + Prime[n]^2; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%t Module[{nn=9600000},Prime[#]&/@Transpose[Select[Thread[{Range[nn], 1+ Accumulate[ Prime[Range[nn]]^2]}],IntegerQ[Last[#]/First[#]]&]][[1]]] (* _Harvey P. Dale_, Sep 09 2014 *)
%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^2); 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 16 2013
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