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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}.

%I A102337 #19 Feb 18 2025 04:03:56
%S A102337 166392559,337149859,1356705139,1455488059,1879518709,2339605519,
%T A102337 2410687039,2811378079,3191346019,3250560139,3442915309,3573582079,
%U A102337 4873308619,4875167959,5362448719,5524743379,5580251359,5716641649,5783545759,5977816549,6019275469,6076905349
%N 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}.
%C A102337 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.
%H A102337 Amiram Eldar, <a href="/A102337/b102337.txt">Table of n, a(n) for n = 1..2500</a>
%F A102337 a(n) == 19 (mod 30). - _Amiram Eldar_, Feb 18 2025
%e A102337 1455488059 is a prime, followed by consecutive prime difference pattern: {4,8,16,32,64}. The terminal prime is 1455488183.
%t A102337 Select[Partition[Prime[Range[3*10^7]], 6, 1], Differences[#] == 2^Range[2, 6] &][[;;, 1]] (* _Amiram Eldar_, Feb 18 2025 *)
%o A102337 (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
%Y A102337 Cf. A001223, A022008, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A102331, A102332, A102333, A102334, A102335, A102336.
%K A102337 nonn
%O A102337 1,1
%A A102337 _Labos Elemer_, Jan 07 2005
%E A102337 a(5)-a(18) from _Donovan Johnson_, Apr 17 2010
%E A102337 a(19)-a(22) from _Amiram Eldar_, Feb 18 2025