A102331 Initial members of quintuplets (p, p+4, p+12, p+16, p+24) of consecutive primes with the corresponding difference pattern is {4,8,4,8}.

13147, 14407, 114757, 132607, 231547, 353317, 459607, 476587, 568987, 601747, 652357, 724627, 794137, 861547, 904777, 1010407, 1094437, 1140847, 1147567, 1170007, 1270417, 1424557, 1441327, 1477027, 1604497, 1646287, 1673377, 2043397, 2078707, 2126767, 2130367

Offset: 1

Author

Labos Elemer, Jan 07 2005

Keywords

• nonn

Comments

Generalization of A022007. These primes are congruent to 7 modulo 10, so the realization of longer prime-difference pattern = {4,8,4,8,4} is not already possible because the sum = 4+8+4+8+4 = 28. Consequently, 10k+7+28 = 10m+5 cannot be a prime. Thus analogous generalization of A022008 is possible only with restrictions. See also Comment in A102335.

Examples

			The prime 13147 is followed by the primes {13151, 13159, 13163, 13171}. Observe that these patterns start and end with primes of the form 10k+7 and 10m+1, respectively.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A022007, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A102335.

Programs

Mathematica

Select[Partition[Prime[Range[158000]], 5, 1], Differences[#] == {4, 8, 4, 8} &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 8 && p4 - p3 == 4 && p5 - p4 == 8, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 18 2025