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 1-7 of 7 results.

A053323 First differences of A031928.

Original entry on oeis.org

42, 60, 42, 54, 72, 12, 126, 30, 54, 60, 18, 78, 24, 18, 90, 102, 18, 12, 102, 18, 78, 150, 72, 156, 72, 24, 78, 78, 138, 12, 24, 36, 54, 378, 126, 72, 12, 36, 120, 30, 84, 108, 252, 156, 30, 24, 12, 126, 60, 54, 30, 348, 18, 12, 12, 18, 12, 54, 12, 24, 120, 180, 198, 48
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Comments

Minimal value is 12; a(n) = 12 for n = 6, 22, 128, 172, 218, 229, 248, 253, 320, 344. - Zak Seidov, Jun 12 2017

Links

Crossrefs

Cf. A031928, A079033.
Cf. A053321, A053322, A053324, A053325, A053326, A053327, A053331.

Programs

  • Mathematica
    Differences[Select[Partition[Prime[Range[800]],2,1],#[[2]]-#[[1]]==10&][[All,1]]] (* Harvey P. Dale, Jan 16 2017 *)

A052352 Least prime in A031924 (lesser of 6-twins) such that the distance to the next 6-twin is 2*n.

Original entry on oeis.org

47, 23, 73, 61, 353, 31, 233, 131, 331, 653, 2441, 3733, 1033, 4871, 1063, 1621, 503, 607, 4211, 7823, 2287, 83, 383, 1231, 2903, 5981, 1123, 173, 11981, 11833, 1367, 2063, 4723, 19681, 2207, 2131, 2713, 9533, 6571, 1657, 23081, 15913, 7013, 14051, 9967, 22447
Offset: 3

Views

Author

Labos Elemer, Mar 07 2000

Keywords

Comments

The increment of distance of 6-twins (A053321) is 2 (not 6), the smallest distance (A052380) is 6.
The middle gap 2n-6 may include primes, e.g., n = 12, a(12) = 653 and between 659 and 659 + 2*12 - 6 = 677, two primes occur (661 and 673).
a(n) = p yields a prime quadruple [p, p+6, p+2n, p+2n+6] with difference pattern [6, 2n-6, 6].

Examples

			For n = 3, 4, 5,  the quadruples are [47, 53, 53, 59] (a triple), [23, 29, 31, 37], [73, 79, 83, 89] with 53 - 47 = 6, 31 - 23 = 8 and 83 - 73 = 10 twin distances.

Links

Crossrefs

Cf. A031924, A052380, A052381, A053321.
Cf. A052350, A052351, A052353, A052354, A052355, A052356, A052357, A052358, A052359.

Programs

  • Mathematica
    seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 6] // Flatten; pp = p[[i]]; dd = Differences[pp]/2 - 2; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[10000] (* Amiram Eldar, Mar 04 2025 *)
  • PARI
    list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 11, , if(p2 == p1 + 6, q2 = p1; if(q1 > 0, d = (q2 - q1)/2 - 2; if(d <= len && s[d] == 0, c++; s[d] = q1; if(c == len, return(s)))); q1 = q2); p1 = p2);} \\ Amiram Eldar, Mar 04 2025

Extensions

Name and offset corrected by Amiram Eldar, Mar 04 2025

A053325 First differences of A031932.

Original entry on oeis.org

180, 24, 456, 66, 24, 90, 456, 174, 264, 192, 318, 66, 210, 120, 66, 120, 84, 570, 84, 102, 54, 30, 276, 354, 324, 72, 84, 180, 156, 24, 336, 270, 114, 666, 324, 150, 90, 324, 96, 24, 126, 186, 108, 126, 24, 150, 162, 528, 186, 54, 120, 90, 300, 456, 120, 150
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Links

Crossrefs

Cf. A031932.
Cf. A053321, A053322, A053323, A053324, A053326, A053327, A053331.

Programs

  • Mathematica
    Differences[Transpose[Select[Partition[Prime[Range[1500]],2,1], Last[#]- First[#] == 14&]][[1]]] (* Harvey P. Dale, Aug 24 2012 *)

A053322 First differences of A031926.

Original entry on oeis.org

270, 30, 12, 48, 30, 12, 192, 18, 18, 24, 18, 150, 18, 54, 126, 54, 30, 180, 66, 84, 36, 12, 162, 90, 156, 24, 150, 60, 30, 30, 186, 72, 78, 54, 36, 42, 102, 36, 30, 102, 30, 168, 12, 228, 42, 132, 78, 18, 162, 408, 60, 234, 168, 192, 108, 120, 18, 210, 174, 120, 90
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Comments

Minimal value 12 is for n = 3, 6, 22, 43, 90, 123, 125, 135, 144, 147, 201, 255, 276, 287, 310, 338, 350. - Zak Seidov, Jun 12 2017

Links

Crossrefs

Cf. A031926.
Cf. A053321, A053323, A053324, A053325, A053326, A053327, A053331.

Programs

  • Mathematica
    With[{p = Prime[Range[1000]]}, Differences[p[[Position[Differences[p], 8] // Flatten]]]] (* Amiram Eldar, Mar 10 2025 *)

A053324 First differences of A031930.

Original entry on oeis.org

12, 256, 42, 110, 42, 136, 200, 204, 36, 70, 152, 40, 12, 20, 178, 80, 22, 78, 180, 30, 198, 102, 48, 132, 42, 156, 150, 122, 18, 102, 22, 68, 72, 16, 152, 60, 100, 272, 58, 90, 20, 298, 12, 140, 130, 12, 110, 76, 42, 120, 48, 110, 64, 158, 88, 320, 100, 174, 50
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Links

Crossrefs

Cf. A031930.
Cf. A053321, A053322, A053323, A053325, A053326, A053327, A053331.

Programs

  • Mathematica
    Differences[Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]]==12&][[;;,1]]] (* Harvey P. Dale, Sep 28 2024 *)

A053326 First differences of A031934.

Original entry on oeis.org

102, 180, 108, 30, 342, 210, 318, 252, 18, 42, 210, 414, 54, 456, 54, 402, 258, 342, 258, 756, 126, 78, 42, 450, 84, 576, 588, 66, 366, 228, 420, 246, 366, 240, 354, 90, 240, 156, 150, 198, 510, 246, 96, 828, 156, 60, 36, 870, 180, 114, 54, 660, 600, 522, 330
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Links

Crossrefs

Cf. A031934.
Cf. A053321, A053322, A053323, A053324, A053325, A053327, A053331.

Programs

  • Mathematica
    With[{p = Prime[Range[2000]]}, Differences[p[[Position[Differences[p], 16] // Flatten]]]] (* Amiram Eldar, Mar 10 2025 *)

A053327 First differences of A031936.

Original entry on oeis.org

546, 190, 122, 378, 154, 248, 342, 358, 942, 86, 270, 214, 50, 40, 140, 100, 30, 326, 150, 274, 528, 218, 222, 78, 52, 38, 540, 192, 42, 40, 26, 162, 262, 308, 570, 348, 184, 456, 200, 244, 498, 62, 378, 1488, 52, 50, 42, 160, 60, 780, 78, 42, 128, 22, 270, 66
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Links

Crossrefs

Cf. A031936.
Cf. A053321, A053322, A053323, A053324, A053325, A053326, A053331.

Programs

  • Mathematica
    With[{p = Prime[Range[2000]]}, Differences[p[[Position[Differences[p], 18] // Flatten]]]] (* Amiram Eldar, Mar 10 2025 *)
Showing 1-7 of 7 results.

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