A078957 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,6).

12637, 14737, 15787, 17467, 78787, 95257, 104707, 120997, 154057, 243517, 250027, 252877, 351037, 357667, 443227, 496477, 501187, 593497, 624787, 696607, 750787, 917827, 949957, 1003087, 1025257, 1104097, 1109887, 1260877, 1279657, 1457857, 1517917, 1565167, 1654717

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+22 are consecutive primes.

Examples

			15787 is in the sequence since 15787, 15791 = 15787 + 4, 15797 = 15787 + 10, 15803 = 15787 + 16 and 15809 = 15787 + 22 are consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

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

Programs

Mathematica

Select[Partition[Prime[Range[10^5]],5,1],Differences[#]=={4,6,6,6}&][[All,1]] (* Harvey P. Dale, Jun 23 2019 *)

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 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002