A078948 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,2).

29, 59, 269, 1289, 2129, 2789, 5639, 8999, 13679, 14549, 18119, 36779, 62129, 75989, 80669, 83219, 88799, 93479, 113159, 115769, 124769, 132749, 150209, 160079, 163979, 203309, 207509, 223829, 228509, 278489, 282089, 284729, 298679, 312929, 313979, 323369, 337859

Offset

1,1

Comments

Equivalently, primes p such that p, p+2, p+8, p+12 and p+14 are consecutive primes.

All terms are congruent to 29 (mod 30). - Muniru A Asiru, Sep 04 2017

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from R. J. Mathar)

R. J. Mathar, Table of Prime Gap Constellations.

Example

59 is in the sequence since 59, 61 = 59 + 2, 67 = 59 + 8, 71 = 59 + 12 and 73 = 59 + 14 are consecutive primes.

Maple

for i from 1 to 10^5 do if [ithprime(i+1), ithprime(i+2), ithprime(i+3), ithprime(i+4)] = [ithprime(i)+2, ithprime(i)+8, ithprime(i)+12, ithprime(i)+14] then print(ithprime(i)); fi; od;  # Muniru A Asiru, Sep 04 2017

Mathematica

Select[Partition[Prime[Range[26000]], 5, 1], Differences[#]=={2, 6, 4, 2}&][[;; , 1]] (* Harvey P. Dale, Dec 10 2024 *)

Prog

(GAP)
K:=26*10^7+1;; # to get all terms <= K.
P:=Filtered([1, 3..K], IsPrime);;  I:=[2, 6, 4, 2];;
P1:=List([1..Length(P)-1], i->P[i+1]-P[i]);;
Q:=List(Positions(List([1..Length(P)-Length(I)], i->[P1[i], P1[i+1], P1[i+2], P1[i+3]]), I), i->P[i]); # Muniru A Asiru, Sep 04 2017
(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 6 && p4 - p3 == 4 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025

Crossrefs

Subsequence of A078848. - R. J. Mathar, Feb 10 2013

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

Sequence in context: A104119 A356717 A042674 * A269263 A042676 A124643

Adjacent sequences: A078945 A078946 A078947 * A078949 A078950 A078951

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved