

A338989


a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is q*(q+1) where q is prime, or 0 if there is no such p.


2



5, 71, 3, 977, 37, 7829, 8681, 283, 14341, 37181, 31, 8839, 1181, 60901, 54727, 2579, 64901, 1248019, 43, 141803, 47, 29881, 991, 5, 881, 1603919, 31123, 18679, 174149, 74149, 11, 1328269, 925513, 447859, 61, 890969, 5867, 35759, 4093, 27239, 1549, 6551, 1901987, 4597, 64781, 307, 13121, 353
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OFFSET

1,1


LINKS

Robert Israel, Table of n, a(n) for n = 1..141


EXAMPLE

a(3) = 3 because the sum of the 2*3=6 consecutive primes starting at 3 is 3+5+7+11+13+17 = 56 = 7*(7+1) where 7 is prime.
a(4) = 977 because the sum of the 2*4=8 consecutive primes starting at 977 is 977+983+991+997+1009+1013+1019+1021 = 8010 = 89*(89+1) where 89 is prime.


MAPLE

N:= 10^5:
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
S:= ListTools:PartialSums([0, op(P)]):
nP:= nops(S):
f:= proc(n) local i;
for i from 1 to nPn do
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
od;
FAIL
end proc:
R:= NULL:
for i from 1 do
v:= f(2*i);
if v = FAIL then break fi;
R:= R, v
od:
R;


CROSSREFS

Cf. A338985, A338990.
Sequence in context: A015502 A303291 A324229 * A101019 A056266 A248367
Adjacent sequences: A338986 A338987 A338988 * A338990 A338991 A338992


KEYWORD

nonn


AUTHOR

J. M. Bergot and Robert Israel, Dec 20 2020


STATUS

approved



