A376892 Numbers k such that the sum of the first k greater of twin primes is a greater of twin prime.

1, 45, 105, 675, 987, 1431, 1593, 1677, 1785, 1875, 2037, 2541, 3039, 3045, 3051, 3183, 3267, 3531, 3699, 4113, 4239, 4377, 4443, 5643, 5673, 5709, 6027, 6543, 6615, 6771, 6891, 6915, 6999, 8043, 8109, 8313, 8607, 8739, 10197, 10569, 11103, 11139, 11361, 11787, 12045

Offset: 1

Author

Ilya Gutkovskiy, Oct 08 2024

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes.

Crossrefs

Cf. A006512, A013916, A071149, A086168, A089228, A376891.

Programs

Maple

K:= 1: count:= 1: s:= 5: k:= 1:
for p from 7 by 6 do
  if isprime(p) and isprime(p-2) then
    k:= k+1;
    s:= s+p;
    if s mod 6 = 1 and isprime(s) and isprime(s-2) then
      count:= count+1; K:= K, k;
      if count = 100 then break fi;
fi fi od:
K; # Robert Israel, Nov 08 2024

PARI

lista(nn) = my(v=select(p->isprime(p-2), primes(nn)), s = vector(#v)); s[1] = v[1]; for (i=2, #v, s[i] = s[i-1]+v[i]); Vec(select(x->(isprime(x) && isprime(x-2)), s, 1)); \\ Michel Marcus, Oct 10 2024