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

%I A376892 #13 Nov 09 2024 06:37:53
%S A376892 1,45,105,675,987,1431,1593,1677,1785,1875,2037,2541,3039,3045,3051,
%T A376892 3183,3267,3531,3699,4113,4239,4377,4443,5643,5673,5709,6027,6543,
%U A376892 6615,6771,6891,6915,6999,8043,8109,8313,8607,8739,10197,10569,11103,11139,11361,11787,12045
%N A376892 Numbers k such that the sum of the first k greater of twin primes is a greater of twin prime.
%H A376892 Robert Israel, <a href="/A376892/b376892.txt">Table of n, a(n) for n = 1..10000</a>
%H A376892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>.
%p A376892 K:= 1: count:= 1: s:= 5: k:= 1:
%p A376892 for p from 7 by 6 do
%p A376892   if isprime(p) and isprime(p-2) then
%p A376892     k:= k+1;
%p A376892     s:= s+p;
%p A376892     if s mod 6 = 1 and isprime(s) and isprime(s-2) then
%p A376892       count:= count+1; K:= K, k;
%p A376892       if count = 100 then break fi;
%p A376892 fi fi od:
%p A376892 K; # _Robert Israel_, Nov 08 2024
%o A376892 (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
%Y A376892 Cf. A006512, A013916, A071149, A086168, A089228, A376891.
%K A376892 nonn
%O A376892 1,2
%A A376892 _Ilya Gutkovskiy_, Oct 08 2024