cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A102334 Initial terms of quintuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48}. The corresponding difference-pattern is {16,8,16,8}.

Original entry on oeis.org

272863, 274123, 372613, 1394893, 1634293, 2380423, 3846373, 5298523, 5358013, 5797903, 6741913, 7554823, 7647643, 7716103, 7738153, 8241463, 8358283, 9710473, 9859783, 12454333, 12510193, 12796423, 13710133, 14477893, 15162493, 15186583, 15263503, 15603853, 16438243, 16771933, 17913283, 18957973, 19373623
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of A022007.

Links

Crossrefs

Cf. A001223, A022007, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A052378, A067140, A067141, A102332, A102333.

Programs

  • Mathematica
    Select[Partition[Prime[Range[1233300]], 5, 1], Differences[#] == {16, 8, 16, 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 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 13 (mod 30). - Amiram Eldar, Feb 18 2025

Extensions

Missing terms a(1)-a(11) inserted by Amiram Eldar, Feb 18 2025

A102335 Initial terms of sextuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48, p+64}. The corresponding difference-pattern is {16,8,16,8,16}.

Original entry on oeis.org

12454333, 21228553, 25131193, 38589673, 41426353, 46254253, 56564623, 60498133, 61151863, 96691213, 158497153, 169760713, 182960473, 201513133, 226086283, 236031463, 253806913, 290686483, 305472373, 344550643, 369110983, 380973253, 421335883, 445537333, 461955763
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of A022008. The generalized pattern of consecutive prime-differences is {6a+4, 6b+2, 6c+4, 6d+2, 6e+4} with a = c = e = 2, b = d = 1.

Links

Crossrefs

Cf. A001223, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A052378, A067140, A067141, A102332, A102333, A102334.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[20000000]],6,1],Differences[#] == {16,8,16,8,16}&]][[1]] (* Harvey P. Dale, Nov 08 2011 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8 && p6 - p5 == 16, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 73 (mod 210). - 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

Views

Author

Labos Elemer, Jan 07 2005

Keywords

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

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

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

Views

Author

Labos Elemer, Jan 07 2005

Keywords

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.

Examples

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

Links

Crossrefs

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

Programs

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

Formula

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

Extensions

a(5)-a(18) from Donovan Johnson, Apr 17 2010
a(19)-a(22) from Amiram Eldar, Feb 18 2025
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.