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 21-30 of 30 results.

A078962 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,2,6).

Original entry on oeis.org

61, 2371, 5431, 11821, 21481, 37561, 50581, 69991, 124291, 126481, 139291, 223831, 230761, 268771, 272341, 275911, 305401, 363361, 365461, 388471, 498391, 516151, 556261, 561091, 585031, 752281, 776551, 783781, 812341, 832621, 911161, 942031, 950221, 1030021, 1108561
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+10, p+12 and p+18 are consecutive primes.

Examples

			61 is in the sequence since 61, 67 = 61 + 6, 71 = 61 + 10, 73 = 61 + 12 and 79 = 61 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078855. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,4,2,6} &][[;;, 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 == 4 && p4 - p3 == 2 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 1 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078963 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,2).

Original entry on oeis.org

3313, 4993, 5851, 9613, 17971, 23011, 32353, 36913, 45121, 51421, 53881, 54403, 59611, 76243, 90001, 91951, 127591, 130633, 131431, 134353, 140401, 142963, 174061, 229753, 246913, 267661, 303361, 311551, 321313, 340111, 386143, 435553, 465061, 514513, 532993, 618571
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+10, p+16 and p+18 are consecutive primes.

Examples

			23011 is in the sequence since 23011, 23017 = 23011 + 6, 23021 = 23011 + 10, 23027 = 23011 + 16 and 23029 = 23011 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078856. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Maple
    L:= [2,3,5,7,11]:
count:= 0: Res:= NULL:
while count < 50 do
  L:= [op(L[2..5]),nextprime(L[5])];
  if L - [L[1]$5] = [0,6,10,16,18] then
    count:= count+1;
    Res:= Res, L[1];
  fi
od:
Res; # Robert Israel, Jun 04 2018
  • Mathematica
    Transpose[Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={6,4,6,2}&]][[1]]  (* Harvey P. Dale, Mar 04 2011 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

From Amiram Eldar, Feb 22 2025: (Start)
a(n) == 1 (mod 6).
a(n) == 1 or 13 (mod 30). (End)

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078964 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,6).

Original entry on oeis.org

157, 4441, 6961, 8731, 14731, 16411, 16921, 20107, 25447, 39097, 47287, 47491, 60601, 78157, 78781, 84121, 92347, 104701, 114067, 115321, 128467, 142537, 183571, 186097, 194707, 196171, 253417, 279121, 286477, 297607, 307267, 327001, 350437, 351031, 354307, 357661
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+10, p+16 and p+22 are consecutive primes.

Examples

			157 is in the sequence since 157, 163 = 157 + 6, 167 = 157 + 10, 173 = 157 + 16 and 179 = 157 + 22 are consecutive primes.

Links

Crossrefs

Subsequence of A078856. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,4,6,6} &][[;;, 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 == 4 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

From Amiram Eldar, Feb 22 2025: (Start)
a(n) == 1 (mod 6).
a(n) == 1 or 7 (mod 30). (End)

Extensions

Edited by Dean Hickerson, Dec 20 2002

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

A078966 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,4,2).

Original entry on oeis.org

601, 2671, 20341, 24091, 41941, 42391, 55201, 65701, 87541, 125101, 198811, 249421, 355501, 414691, 416401, 428551, 510061, 521161, 541531, 543871, 560221, 603901, 609601, 637711, 663961, 669661, 743161, 770041, 986131, 1020961, 1026661, 1099711, 1113181, 1120501
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+12, p+16 and p+18 are consecutive primes.

Examples

			601 is in the sequence since 601, 607 = 601 + 6, 613 = 601 + 12, 617 = 601 + 16 and 619 = 601 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078858. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[81000]],5,1],Differences[#] == {6,6,4,2}&]][[1]] (* Harvey P. Dale, Sep 15 2011 *)
  • 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 == 4 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 1 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078967 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,4,6).

Original entry on oeis.org

151, 367, 3307, 4987, 20101, 30097, 52951, 53617, 85831, 92221, 95701, 99817, 103561, 128461, 135601, 163621, 214651, 221071, 241321, 241861, 246907, 274831, 280591, 282691, 287851, 294787, 295831, 297601, 307261, 308311, 334771, 340897, 347161, 350431, 354301
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+12, p+16 and p+22 are consecutive primes.

Examples

			151 is in the sequence since 151, 157 = 151 + 6, 163 = 151 + 12, 167 = 151 + 16 and 173 = 151 + 22 are consecutive primes.

Links

Crossrefs

Subsequence of A078858. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[30000]],5,1],Differences[#] == {6,6,4,6}&]][[1]] (* Harvey P. Dale, Apr 06 2012 *)
  • 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 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

From Amiram Eldar, Feb 22 2025: (Start)
a(n) == 1 (mod 6).
a(n) == 1 or 7 (mod 30). (End)

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078968 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,6,2).

Original entry on oeis.org

251, 17471, 56081, 75521, 94421, 115751, 121001, 154061, 163841, 179801, 185051, 250031, 344231, 351041, 380441, 417941, 517061, 683681, 703211, 713171, 783131, 849581, 916451, 983771, 1003091, 1025261, 1055591, 1070411, 1115561, 1129841, 1260881, 1517921, 1565171
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+12, p+18 and p+20 are consecutive primes.

Examples

			251 is in the sequence since 251, 257 = 251 + 6, 263 = 251 + 12, 269 = 251 + 18 and 271 = 251 + 20 are consecutive primes.

Links

Crossrefs

Subsequence of A033451. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[150000]], 5, 1], Differences[#] == {6,6,6,2} &][[;;, 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 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 11 (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.

A078960 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,6).

Original entry on oeis.org

593, 4643, 6353, 11483, 19463, 34253, 71333, 77543, 89513, 101273, 135593, 148853, 179813, 184823, 191453, 193373, 245513, 260003, 267893, 277883, 280583, 302573, 307253, 308303, 310223, 344243, 346433, 350423, 376463, 408203, 416393, 435563, 442823, 450473, 482393
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+8, p+14 and p+20 are consecutive primes.

Examples

			593 is in the sequence since 593, 599 = 593 + 6, 601 = 593 + 8, 607 = 593 + 14 and 613 = 593 + 20 are consecutive primes.

Links

Crossrefs

Subsequence of A078854. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[36000]],5,1],Differences[#]=={6,2,6,6}&]][[1]] (* Harvey P. Dale, Oct 14 2013 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 2 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 23 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A342502 Gaps between first elements of prime quintuples of the form (p, p+2, p+6, p+12, p+14). The quintuples are abutting: twin/cousin/sexy/twin pairs.

Original entry on oeis.org

12, 210, 1050, 330, 1920, 390, 720, 150, 22950, 10710, 780, 5040, 27060, 26040, 2340, 13440, 8880, 360, 1950, 41370, 17790, 3630, 4320, 6510, 870, 76620, 15210, 21540, 5760, 29100, 2340, 66990, 1950, 3360, 5370, 16800, 6930, 40530, 4230, 3570, 15510, 10320
Offset: 1

Views

Author

James S. DeArmon, Mar 14 2021

Keywords

Examples

			The first 4 terms of the sequence are 12, 210, 1050, 330, since the gaps between first elements of the first five quintuples {5,7,11,17,19}, {17,19,23,29,31}, {227,229,233,239,241}, {1277,1279,1283,1289,1291}, {1607,1609,1613,1619,1621} are, 17-5=12, 227-17=210, etc.

Links

Crossrefs

Cf. A078946.

Programs

  • Maple
    b:= proc(n) option remember; local p; p:= `if`(n=1, 1, b(n-1));
      do p:= nextprime(p);
         if andmap(isprime, [p+2, p+6, p+12, p+14]) then return p fi
      od
    end:
a:= n-> b(n+1)-b(n):
seq(a(n), n=1..65);  # Alois P. Heinz, Mar 14 2021
  • Mathematica
    b[n_] := b[n] = Module[{p}, p = If[n == 1, 1, b[n-1]]; While[True, p = NextPrime[p]; If[AllTrue[{p+2, p+6, p+12, p+14}, PrimeQ], Return[p]]]];
a[n_] := b[n+1]-b[n];
Table[a[n], {n, 1, 65}] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)

Formula

a(n) = A078946(n) - A078946(n-1) for n >= 2.
a(n) == 0 (mod 30) for n>1.
Previous Showing 21-30 of 30 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.