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 1-8 of 8 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 *)

A052356 Least prime in A031932 (lesser of 14-twins) whose distance to the next 14-twin is 6*n.

Original entry on oeis.org

24749, 293, 3833, 21467, 23417, 14159, 3779, 18353, 773, 4817, 18959, 2939, 863, 7607, 3677, 8039, 5939, 2633, 7727, 13367, 51839, 51659, 7043, 5153, 8447, 26189, 1409, 113, 7853, 1847, 13859, 43223, 2423, 24533, 65867, 50909, 19763, 15173, 15527, 86477, 55229
Offset: 3

Views

Author

Labos Elemer, Mar 07 2000

Keywords

Comments

The smallest distance between 14-twins [A052380(7)] is 18 and its minimal increment is 6.
a(n) = p is the first prime initiating [p, p+14, p+6n, p+6n+14] quadruple and prime difference pattern of [14, 6n-14, 14].

Examples

			n = 4 results in [293,307,317,331] primes pattern and [14,24,14] difference pattern with 2 further primes (311 and 313) in the central gap.

Links

Crossrefs

Cf. A031932, A052380, A052381, A053325.
Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052357, A052358, A052359.

Programs

  • Mathematica
    seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 14] // Flatten; pp = p[[i]]; dd = Differences[pp]/6 - 2; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[10000] (* 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 + 14, q2 = p1; if(q1 > 0, d = (q2 - q1)/6 - 2; 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

Name and offset corrected by Amiram Eldar, Mar 05 2025

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 *)

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 *)

A052377 Primes followed by an [8,4,8]=[d,D-d,d] prime difference pattern of A001223.

Original entry on oeis.org

389, 479, 1559, 3209, 8669, 12269, 12401, 13151, 14411, 14759, 21851, 28859, 31469, 33191, 36551, 39659, 40751, 50321, 54311, 64601, 70229, 77339, 79601, 87671, 99551, 102539, 110261, 114749, 114761, 118661, 129449, 132611, 136511
Offset: 1

Views

Author

Labos Elemer, Mar 22 2000

Keywords

Comments

A subsequence of A031926. [Corrected by Sean A. Irvine, Nov 07 2021]
a(n)=p, the initial prime of two consecutive 8-twins of primes as follows: [p,p+8] and [p+12,p+12+8], d=8, while the distance of the two 8-twins is 12 (minimal; see A052380(4/2)=12).
Analogous sequences are A047948 for d=2, A052378 for d=4, A052376 for d=10 and A052188-A052199 for d=6k, so that in the [d,D-d,d] difference patterns which follows a(n) the D-d is minimal(=0,2,4; here it is 4).

Examples

			p=1559 begins the [1559,1567,1571,1579] prime quadruple consisting of two 8-twins [1559,1567] and[1571,1579] which are in minimal distance, min{D}=1571-1559=12=A052380(8/2).

Crossrefs

Cf. A031926, A053325, A052380, A052376, A052378, A052188-A052190.

Formula

a(n) is the initial term of a [p, p+8, p+12, p+12+8] quadruple of consecutive primes.
Showing 1-8 of 8 results.

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