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A338990
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.
2
19, 61, 17, 8581, 10883, 151, 2083, 21859, 11813, 443, 6779, 1531, 21559, 37781, 7529, 757, 29027, 2591, 12739, 1637, 491, 4759, 56269, 341179, 37441, 81547, 59, 229, 1814023, 363523, 12109, 21493, 247993, 248089, 3617, 357551, 3109, 138563, 66973, 100103, 6907, 44819, 136519, 2953, 13063, 31687
OFFSET
1,1
LINKS
EXAMPLE
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.
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 nP-n 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
Sequence in context: A270818 A206426 A211145 * A158521 A141897 A031384
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 20 2020
STATUS
approved