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.

Previous Showing 11-17 of 17 results.

A078850 Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[4,2,6]; short d-string notation of pattern = [426].

Original entry on oeis.org

67, 1447, 2377, 2707, 5437, 5737, 7207, 9337, 11827, 12037, 19207, 21487, 21517, 23197, 26107, 26947, 28657, 31147, 31177, 35797, 37357, 37567, 42697, 50587, 52177, 65167, 67927, 69997, 71707, 74197, 79147, 81547, 103087, 103387, 106657
Offset: 1

Views

Author

Labos Elemer, Dec 11 2002

Keywords

Comments

Subsequence of A022005. - R. J. Mathar, May 06 2017

Examples

			p=67,67+4=71,67+4+2=73,67+4+2+6=79 are consecutive primes.

Links

Crossrefs

Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].

Programs

  • Mathematica
    d = {4, 2, 6}; First /@ Select[Partition[Prime@ Range@ 12000, Length@ d + 1, 1], Differences@ # == d &] (* Michael De Vlieger, May 02 2016 *)

Formula

Primes p = p(i) such that p(i+1)=p+4, p(i+2)=p+4+2, p(i+3)=p+4+2+6.

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

A132259 Isolated primes congruent to {1, 17, 19, 29} mod 30.

Original entry on oeis.org

47, 79, 89, 167, 211, 257, 317, 331, 359, 379, 389, 409, 439, 449, 467, 479, 499, 509, 541, 557, 587, 631, 647, 677, 691, 709, 719, 739, 751, 769, 797, 839, 887, 919, 929, 947, 977, 991, 1009, 1039, 1069, 1097, 1109, 1129, 1171, 1187
Offset: 1

Views

Author

Omar E. Pol, Aug 20 2007

Keywords

Links

Crossrefs

Cf. A007510, A074822, A078857.

Programs

  • Mathematica
    Select[Prime[Range[200]],NoneTrue[#+{2,-2},PrimeQ]&&MemberQ[ {1,17,19,29},Mod[ #,30]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 04 2019 *)

A078965 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,2,6).

Original entry on oeis.org

47, 257, 557, 587, 1217, 4007, 6257, 10847, 14537, 17477, 19457, 26717, 41597, 51407, 84047, 94427, 101267, 115757, 131927, 150077, 150197, 154067, 169307, 179807, 185057, 193367, 206807, 250037, 267887, 275147, 290027, 302567, 344237, 408197, 428027, 442817, 443147
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+12, p+14 and p+20 are consecutive primes.

Examples

			257 is in the sequence since 257, 263 = 257 + 6, 269 = 257 + 12, 271 = 257 + 14 and 277 = 257 + 20 are consecutive primes.

Links

Crossrefs

Subsequence of A078857. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,6,2,6} &][[;;, 1]] (* Amiram Eldar, Feb 22 2025 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 17 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A079017 Suppose p and q = p+14 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 15 possible difference patterns, namely [14], [2,12], [6,8], [8,6], [12,2], [2,4,8], [2,6,6], [2,10,2], [6,2,6], [6,6,2], [8,4,2], [2,4,6,2], [2,6,4,2], [2,2,4,2,4], [2,4,2,4,2]. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.

Original entry on oeis.org

3, 5, 17, 23, 29, 47, 83, 89, 113, 137, 149, 197, 359, 509, 1997
Offset: 1

Views

Author

Labos Elemer, Jan 24 2003

Keywords

Examples

			p=1997, q=2011 has difference pattern [2,4,8] and {1997,1999,2003,2011} is the corresponding consecutive prime 4-tuple.

Crossrefs

A022006(1)=5, A022007(1)=7, A078847(1)=17, A078851(1)=19, A078946(1)=17, A078854(1)=23, A078948(1)=29, A078857(1)=47, A031932(1)=113, A078849(1)=149.
Cf. A079016-A079024.

A132255 Isolated primes congruent to {17, 19} mod 30.

Original entry on oeis.org

47, 79, 167, 257, 317, 379, 409, 439, 467, 499, 557, 587, 647, 677, 709, 739, 769, 797, 887, 919, 947, 977, 1009, 1039, 1069, 1097, 1129, 1187, 1217, 1249, 1307, 1367, 1399, 1459, 1549, 1579, 1637, 1759, 1847, 1907, 2179, 2207, 2297
Offset: 1

Views

Author

Omar E. Pol, Aug 20 2007

Keywords

Links

Crossrefs

Cf. A007510, A074822, A078857.

Programs

  • Mathematica
    Select[Prime[Range[500]],NoneTrue[#+{2,-2},PrimeQ]&&MemberQ[{17,19},Mod[#,30]]&]

A132251 Isolated primes congruent to 17 (mod 30).

Original entry on oeis.org

47, 167, 257, 317, 467, 557, 587, 647, 677, 797, 887, 947, 977, 1097, 1187, 1217, 1307, 1367, 1637, 1847, 1907, 2207, 2297, 2357, 2417, 2447, 2477, 2777, 2837, 2897, 2927, 2957, 3137, 3347, 3407, 3617, 3677, 3797, 3947, 4007, 4397
Offset: 1

Views

Author

Omar E. Pol, Aug 20 2007

Keywords

Links

Crossrefs

Cf. A007510, A078857.

A132257 Isolated primes congruent to {11, 13, 17, 19} mod 30.

Original entry on oeis.org

47, 79, 131, 163, 167, 223, 251, 257, 317, 373, 379, 401, 409, 439, 467, 491, 499, 557, 587, 613, 647, 673, 677, 701, 709, 733, 739, 761, 769, 797, 853, 887, 911, 919, 941, 947, 971, 977, 1009, 1039, 1069, 1097, 1123, 1129, 1181, 1187
Offset: 1

Views

Author

Omar E. Pol, Aug 20 2007

Keywords

Links

Crossrefs

Cf. A007510, A074822, A078857.
Previous Showing 11-17 of 17 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.