A102337 Initial members of sextuplets (p, p+4, p+12, p+28, p+60, p+124) of consecutive primes with the corresponding difference pattern is {4,8,16,32,64}.

166392559, 337149859, 1356705139, 1455488059, 1879518709, 2339605519, 2410687039, 2811378079, 3191346019, 3250560139, 3442915309, 3573582079, 4873308619, 4875167959, 5362448719, 5524743379, 5580251359, 5716641649, 5783545759, 5977816549, 6019275469, 6076905349

Offset

1,1

Comments

Generalization of A022008 because the relevant prime-difference pattern has the following form: (4+6a,2+6b,4+6c,2+6d,4+6e), a = 0, b = 1, c = 2, d = 5, e = 10. The primes are congruent to 9 modulo 10, while terminal entries of the quintuplets have the form 10s+3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..2500

Formula

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

Example

1455488059 is a prime, followed by consecutive prime difference pattern: {4,8,16,32,64}. The terminal prime is 1455488183.

Mathematica

Select[Partition[Prime[Range[3*10^7]], 6, 1], Differences[#] == 2^Range[2, 6] &][[;; , 1]] (* Amiram Eldar, Feb 18 2025 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 4 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 32 && p6 - p5 == 64, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6); } \\ Amiram Eldar, Feb 18 2025

Crossrefs

Cf. A001223, A022008, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A102331, A102332, A102333, A102334, A102335, A102336.

Sequence in context: A116643 A162839 A251473 * A295456 A172567 A172590

Adjacent sequences: A102334 A102335 A102336 * A102338 A102339 A102340

Keyword

nonn,changed

Author

Labos Elemer, Jan 07 2005

Extensions

a(5)-a(18) from Donovan Johnson, Apr 17 2010

a(19)-a(22) from Amiram Eldar, Feb 18 2025

Status

approved