A102336 Initial members of quintuplets (p, p+4, p+12, p+28, p+60) of consecutive primes with the corresponding difference pattern is {4,8,16,32}.

1197739, 2496409, 2692549, 2962489, 3195679, 5723479, 6824899, 7706059, 8056039, 8337319, 10132609, 10583269, 11739589, 12167509, 12674659, 13007959, 13699459, 14148049, 14252929, 14702839, 15726019, 16694539, 17115949, 17282299, 17350159, 17584729, 18065389, 18097609

Offset: 1

Author

Labos Elemer, Jan 07 2005

Keywords

• nonn

Comments

Generalization of A022007. These primes are congruent to 9 modulo 10, while terminal entry of 5-tuple has the form 10s+9.

Examples

			1197739 is a prime, followed by (1197743, 1197751, 1197767, 1197799) with consecutive prime difference pattern: {4,8,16,32}.
		

Links

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

Crossrefs

Cf. A001223, A022007, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A102331, A102332, A102333, A102334, A102335.

Programs

Mathematica

Select[Partition[Prime[Range[10^6]], 5, 1], Differences[#] == 2^Range[2, 5] &][[;;, 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 == 16 && p5 - p4 == 32, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 19 (mod 30). - Amiram Eldar, Feb 18 2025