%I #12 Oct 16 2024 21:40:36
%S 1,23,143,251,281,305,341,455,605,761,1349,1613,2765,2903,2981,3623,
%T 3725,3923,4049,4133,4745,5207,5303,5489,5765,6515,6611,7793,7835,
%U 8153,8237,10427,10697,11261,11447,11627,11729,12401,12701,13871,14327,15359,15683
%N Numbers k such that the sum of the first k lesser of twin primes is a lesser of twin prime.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>.
%p K:= 1: count:= 1: s:= 3: k:= 1:
%p for p from 5 by 6 do
%p if isprime(p) and isprime(p+2) then
%p k:= k+1;
%p s:= s+p;
%p if s mod 6 = 5 and isprime(s) and isprime(s+2) then
%p count:= count+1; K:= K,k;
%p if count = 100 then break fi;
%p fi fi od:
%p K; # _Robert Israel_, Oct 08 2024
%o (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 Cf. A001359, A013916, A071149, A086167, A089228, A376892.
%K nonn,new
%O 1,2
%A _Ilya Gutkovskiy_, Oct 08 2024