A227063 Prime in the middle of a list of 7 consecutive primes such that each of them is a member of a twin pair.

11, 9433, 9437, 62983, 62987, 72229, 72251, 392269, 392279, 495589, 495611, 663583, 663587, 909301, 909317, 909319, 909329, 1006309, 1006331, 1138393, 1138409, 1159201, 1159229, 1173553, 1173581, 1322161, 1322171, 2144491

Offset

1,1

Comments

This is roughly a search for at least three successive zeros in A048614.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

The twin prime 9433 is in the sequence because it is in the middle of the list of 7 successive primes 9419, 9421, 9431, 9433, 9437, 9439, 9461, of which each is a member of a twin prime pair.

Maple

L:= [seq(ithprime(i), i=1..8)]: Flags:= [false, true$6]: count:= 0: R:= NULL:
while count < 40 do
  L:= [seq(L[i], i=2..8), nextprime(L[8])];
  Flags:= [seq(Flags[i], i=2..7), (L[7]-L[6]=2) or (L[8]-L[7]=2)];
  if Flags = [true$7] then R:= R, L[4]; count:= count+1;  fi
od:
R; # Robert Israel, Mar 05 2025

Mathematica

tp7Q[lst_]:=Total[If[PrimeQ[#+2]||PrimeQ[#-2], 1, 0]&/@lst]==7; Select[Partition[Prime[ Range[ 160000]], 7, 1], tp7Q][[;; , 4]] (* Harvey P. Dale, Oct 22 2023 *)

Crossrefs

Cf. A001097, A048614.

Sequence in context: A080050 A067254 A099806 * A286197 A287078 A286964

Adjacent sequences: A227060 A227061 A227062 * A227064 A227065 A227066

Keyword

nonn,changed

Author

Irina Gerasimova, Jun 30 2013

Status

approved