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}.
Original entry on oeis.org
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
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.
Cf.
A001223,
A022007,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A102335.
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Select[Partition[Prime[Range[158000]], 5, 1], Differences[#] == {4, 8, 4, 8} &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)
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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
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}.
Original entry on oeis.org
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
1197739 is a prime, followed by (1197743, 1197751, 1197767, 1197799) with consecutive prime difference pattern: {4,8,16,32}.
Cf.
A001223,
A022007,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A102331,
A102332,
A102333,
A102334,
A102335.
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Select[Partition[Prime[Range[10^6]], 5, 1], Differences[#] == 2^Range[2, 5] &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)
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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
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}.
Original entry on oeis.org
166392559, 337149859, 1356705139, 1455488059, 1879518709, 2339605519, 2410687039, 2811378079, 3191346019, 3250560139, 3442915309, 3573582079, 4873308619, 4875167959, 5362448719, 5524743379, 5580251359, 5716641649, 5783545759, 5977816549, 6019275469, 6076905349
Offset: 1
1455488059 is a prime, followed by consecutive prime difference pattern: {4,8,16,32,64}. The terminal prime is 1455488183.
Cf.
A001223,
A022008,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A102331,
A102332,
A102333,
A102334,
A102335,
A102336.
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Select[Partition[Prime[Range[3*10^7]], 6, 1], Differences[#] == 2^Range[2, 6] &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)
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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
Showing 1-3 of 3 results.
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