A078963 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,2).

3313, 4993, 5851, 9613, 17971, 23011, 32353, 36913, 45121, 51421, 53881, 54403, 59611, 76243, 90001, 91951, 127591, 130633, 131431, 134353, 140401, 142963, 174061, 229753, 246913, 267661, 303361, 311551, 321313, 340111, 386143, 435553, 465061, 514513, 532993, 618571

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+10, p+16 and p+18 are consecutive primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)

Formula

From Amiram Eldar, Feb 22 2025: (Start)

a(n) == 1 (mod 6).

a(n) == 1 or 13 (mod 30). (End)

Example

23011 is in the sequence since 23011, 23017 = 23011 + 6, 23021 = 23011 + 10, 23027 = 23011 + 16 and 23029 = 23011 + 18 are consecutive primes.

Maple

L:= [2, 3, 5, 7, 11]:
count:= 0: Res:= NULL:
while count < 50 do
  L:= [op(L[2..5]), nextprime(L[5])];
  if L - [L[1]$5] = [0, 6, 10, 16, 18] then
    count:= count+1;
    Res:= Res, L[1];
  fi
od:
Res; # Robert Israel, Jun 04 2018

Mathematica

Transpose[Select[Partition[Prime[Range[50000]], 5, 1], Differences[#]=={6, 4, 6, 2}&]][[1]]  (* Harvey P. Dale, Mar 04 2011 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078856. - R. J. Mathar, May 06 2017

Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Sequence in context: A180679 A251900 A078348 * A236643 A175277 A209206

Adjacent sequences: A078960 A078961 A078962 * A078964 A078965 A078966

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved