A376891 Numbers k such that the sum of the first k lesser of twin primes is a lesser of twin prime.
1, 23, 143, 251, 281, 305, 341, 455, 605, 761, 1349, 1613, 2765, 2903, 2981, 3623, 3725, 3923, 4049, 4133, 4745, 5207, 5303, 5489, 5765, 6515, 6611, 7793, 7835, 8153, 8237, 10427, 10697, 11261, 11447, 11627, 11729, 12401, 12701, 13871, 14327, 15359, 15683
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Twin Primes.
Programs
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Maple
K:= 1: count:= 1: s:= 3: k:= 1: for p from 5 by 6 do if isprime(p) and isprime(p+2) then k:= k+1; s:= s+p; if s mod 6 = 5 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, Oct 08 2024 -
Mathematica
Position[Accumulate[Select[Partition[Prime[Range[200000]],2,1],#[[2]]-#[[1]]==2&][[;;,1]]],?(AllTrue[#+{0,2},PrimeQ]&)]//Quiet//Flatten (* _Harvey P. Dale, Jun 24 2025 *)
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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