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 *)

A052358 Least prime in A031936 (lesser of 18-twins) whose distance to the next 18-twin is 2*n.

Original entry on oeis.org

20183, 20963, 14011, 26759, 7433, 45613, 4703, 21911, 26539, 18233, 6581, 4423, 7351, 37379, 55903, 25801, 4373, 6529, 35879, 119993, 22171, 12923, 10691, 52609, 14303, 20201, 16231, 21121, 103049, 17863, 6451, 34439, 50341, 76129, 3803, 23251, 15241, 14369
Offset: 9

Views

Author

Labos Elemer, Mar 07 2000

Keywords

Comments

The smallest distance between 18-twins [A052380(9)] is 18 and its minimal increment is 2.
a(n) = p is the first prime initiating [p, p+18, p+2n, p+2n+18] prime and [18, 2n-18, 18] d-pattern.

Examples

			a(11) = 14011 initiates prime quadruple [14011, 14029, 14033, 14051] and difference pattern [18, 4, 18].
a(15) = 4703 specifies prime quadruple  [4703, 4721, 4133, 4151] which includes 2 primes (4723, 4729) in the center, and difference pattern [18, 28, 18].

Links

Crossrefs

Cf. A031936, A052380, A052381, A053327.
Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052356, A052357, A052359.

Programs

  • Mathematica
    seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 18] // Flatten; pp = p[[i]]; dd = Differences[pp]/2 - 8; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[12000] (* Amiram Eldar, Mar 05 2025 *)
  • PARI
    list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 18, q2 = p1; if(q1 > 0, d = (q2 - q1)/2 - 8; if(d <= len && s[d] == 0, c++; s[d] = q1; if(c == len, return(s)))); q1 = q2); p1 = p2);} \\ Amiram Eldar, Mar 05 2025

Extensions

a(21) corrected and missing terms inserted by Sean A. Irvine, Nov 07 2021
Name and offset corrected by Amiram Eldar, Mar 05 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 *)

A053321 First differences of A031924.

Original entry on oeis.org

8, 16, 6, 8, 12, 10, 48, 20, 6, 10, 6, 60, 18, 6, 6, 8, 60, 22, 14, 6, 10, 50, 10, 60, 38, 16, 6, 8, 16, 6, 8, 6, 40, 6, 24, 50, 6, 18, 190, 6, 24, 6, 14, 22, 20, 30, 34, 6, 14, 6, 58, 6, 30, 6, 8, 52, 8, 30, 40, 6, 66, 20, 40, 50, 10, 48, 12, 8, 36, 84, 6, 6, 24, 84, 40, 6, 66, 14, 24
Offset: 1

Views

Author

Labos Elemer, Mar 06 2000

Keywords

Links

Crossrefs

Cf. A031924.
Cf. A053322, A053323, A053324, A053325, A053326, A053327, A053331.

Programs

  • GAP
    P:=Filtered([1..2100],IsPrime);;
P1:=List(Filtered([1..Length(P)-1],i->P[i+1]-P[i]=6),k->P[k]);;
a:=List([1..Length(P1)-1],i->P1[i+1]-P1[i]);; Print(a); # Muniru A Asiru, Dec 23 2018
  • Mathematica
    With[{p = Prime[Range[330]]}, Differences[p[[Position[Differences[p], 6] // Flatten]]]] (* Amiram Eldar, Mar 10 2025 *)

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 *)
Showing 1-7 of 7 results.

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