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

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

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

Programs

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 *)

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

Formula

From Amiram Eldar, Feb 22 2025: (Start)

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

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

Extensions

Edited by Dean Hickerson, Dec 20 2002