A078956 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).

43, 163, 643, 1213, 2953, 4003, 7573, 11923, 14533, 25453, 26683, 26713, 29863, 41593, 48523, 61543, 68473, 150193, 151153, 172423, 206803, 227593, 290023, 302563, 338563, 343813, 346543, 428023, 527053, 529033, 540373, 547483, 551713, 570403, 577513, 622603, 628993

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+4, p+10, p+16 and p+18 are consecutive primes.

All terms == 13 (mod 30). - Robert Israel, Oct 17 2023

Examples

			43 is in the sequence since 43, 47 = 43 + 4, 53 = 43 + 10, 59 = 43 + 16 and 61 = 43 + 18 are consecutive primes.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Robert Israel)

Crossrefs

Subsequence of A078852. - R. J. Mathar, May 06 2017

Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.

Programs

Maple

L:= [0$5]:
p:= 1: R:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  L:= [L[2],L[3],L[4],L[5],p];
  if L -~ L[1] = [0, 4, 10, 16, 18] then
    count:= count+1;
    R:= R, L[1];
  fi
od:
R; # Robert Israel, Oct 17 2023

Mathematica

Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={4,6,6,2}&][[All,1]] (* Harvey P. Dale, Jan 23 2021 *)

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002