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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A200845 A235392 A078852 * A206399 A123040 A142016

Adjacent sequences: A078953 A078954 A078955 * A078957 A078958 A078959

Keyword

nonn,changed

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved