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%I #10 Dec 21 2020 02:06:00
%S 19,61,17,8581,10883,151,2083,21859,11813,443,6779,1531,21559,37781,
%T 7529,757,29027,2591,12739,1637,491,4759,56269,341179,37441,81547,59,
%U 229,1814023,363523,12109,21493,247993,248089,3617,357551,3109,138563,66973,100103,6907,44819,136519,2953,13063,31687
%N a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is (q-1)*q where q is prime, or 0 if there is no such p.
%H Robert Israel, <a href="/A338990/b338990.txt">Table of n, a(n) for n = 1..306</a>
%e a(3) = 17 because the sum of the 2*3=6 consecutive primes starting at 17 is 17+19+23+29+31+37 = 156 = 12*13 where 13 is prime.
%p N:= 10^5:
%p P:= select(isprime, [2, seq(i, i=3..N, 2)]):
%p S:= ListTools:-PartialSums([0, op(P)]):
%p nP:= nops(S):
%p f:= proc(n) local i;
%p for i from 1 to nP-n do
%p if issqr(1+4*(S[i+n]-S[i])) and isprime((sqrt(1+4*(S[i+n]-S[i]))+1)/2)then return P[i] fi
%p od;
%p FAIL
%p end proc:
%p R:= NULL:
%p for i from 1 do
%p v:= f(2*i);
%p if v = FAIL then break fi;
%p R:= R, v
%p od:
%p R;
%Y Cf. A338985, A338989.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Dec 20 2020
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