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.

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

Robert Israel, Table of n, a(n) for n = 1..306

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

Cf. A338985, A338989.

Sequence in context: A270818 A206426 A211145 * A158521 A141897 A031384

Adjacent sequences: A338987 A338988 A338989 * A338991 A338992 A338993

Keyword

nonn

Author

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

Status

approved