A348671 a(n) is the least prime p such that there are exactly n primes q < p with 2*p+q prime.

2, 5, 7, 13, 53, 43, 47, 67, 107, 137, 173, 191, 163, 271, 307, 277, 313, 389, 461, 487, 593, 523, 563, 613, 691, 739, 787, 811, 797, 937, 983, 887, 1039, 1069, 997, 1181, 1117, 1249, 1301, 1453, 1303, 1597, 1399, 1483, 1567, 1721, 1871, 1783, 1693, 1697, 1987, 1877, 1847, 2311, 2143, 2309, 2281

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Example

a(3) = 13 because there are 3 primes q < 13 with 2*13+q prime, namely 2*13+3 = 29, 2*13+5 = 31, 2*13+11 = 37, and no prime < 13 has exactly 3 such primes.

Maple

P:= [seq(ithprime(i), i=1..10000)]:
M:= 100: V:= Array(0..M): count:= 0:
for k from 1 to 10000 while count < M+1 do
  v:= nops(select(isprime, {seq(2*P[k]+P[j], j=1..k-1)}));
  if v <= M and V[v] = 0 then
    count:= count+1; V[v]:= P[k];
  fi
od:
convert(V, list);

Mathematica

cnt[p_] := Count[Range[2, p - 1], _?(PrimeQ[#] && PrimeQ[2*p + #] &)]; seq[m_] := Module[{s = Table[0, {m}], c = 0, p = 1, i}, While[c < m, p = NextPrime[p]; i = cnt[p] + 1; If[i <= m && s[[i]] == 0, c++; s[[i]] = p]]; s]; seq[50] (* Amiram Eldar, Dec 13 2021 *)

Crossrefs

Sequence in context: A053647 A023242 A164570 * A265811 A265793 A126338

Adjacent sequences: A348668 A348669 A348670 * A348672 A348673 A348674

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 13 2021

Status

approved