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.

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A078951 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,6,6).

Original entry on oeis.org

3299, 5099, 6359, 19469, 30089, 53609, 63689, 71339, 77549, 80909, 105359, 119549, 152939, 186869, 292469, 302969, 344249, 348239, 408209, 415949, 652739, 707669, 737039, 792689, 818339, 831539, 852749, 886979, 910199, 974969, 1072829, 1152629, 1290629, 1368329
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+2, p+8, p+14 and p+20 are consecutive primes.

Examples

			5099 is in the sequence since 5099, 5101 = 5099 + 2, 5107 = 5099 + 8, 5113 = 5099 + 14 and 5119 = 5099 + 20 are consecutive primes.

Links

Crossrefs

Subsequence of A078849. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 6, 6} &][[;;, 1]] (* Amiram Eldar, Feb 21 2025 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 29 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078952 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,4,6).

Original entry on oeis.org

13, 37, 223, 1087, 1423, 1483, 2683, 4783, 20743, 27733, 29017, 33343, 33613, 35527, 42457, 44263, 45817, 55813, 93487, 108877, 110917, 113143, 118897, 151237, 165703, 187123, 198823, 203653, 205417, 221713, 234187, 234457, 258607, 276817, 284227, 289837, 308923
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+6, p+10 and p+16 are consecutive primes.
All terms = {7, 13} mod 30. - Muniru A Asiru, Aug 21 2017

Examples

			37 is in the sequence since 37, 41 = 37 + 4, 43 = 37 + 6, 47 = 37 + 10 and 53 = 37 + 16 are consecutive primes.

Links

Crossrefs

Subsequence of A052378. - R. J. Mathar, Feb 11 2013
Cf. A001223, A022006, A022007, A078866, A078867, A078946-A078971.

Programs

  • GAP
    K:=2*10^7+1;; # to get all terms <= K.
P:=Filtered([1,3..K],IsPrime);;  I:=[4,2,4,6];;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]);;
P3:=List(Positions(P2,I),i->P[i]); # Muniru A Asiru, Aug 21 2017
  • Maple
    for i from 1 to 10^7 do if ithprime(i+1)=ithprime(i)+4 and ithprime(i+2)=ithprime(i)+6 and ithprime(i+3)=ithprime(i)+10 and ithprime(i+4)=ithprime(i)+16 then print(ithprime(i)); fi; od; # Muniru A Asiru, Aug 21 2017
  • Mathematica
    With[{s = Differences@ Prime@ Range[10^5]}, Prime[SequencePosition[s, {4, 2, 4, 6}][[All, 1]]]] (* Michael De Vlieger, Aug 21 2017 *)
  • PARI
    lista(nn) = forprime(p=3, nn, if(nextprime(p+1)==p+4 && nextprime(p+5)==p+6 && nextprime(p+7)==p+10 && nextprime(p+11)==p+16, print1(p, ", "))); \\ Altug Alkan, Aug 21 2017
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 2 && p4 - p3 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078953 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,6,4).

Original entry on oeis.org

67, 2377, 21487, 31177, 65167, 67927, 81547, 139297, 166597, 178597, 185527, 305017, 305407, 321817, 341947, 390487, 427417, 448867, 547357, 600877, 635347, 668527, 693727, 697507, 752287, 764887, 783787, 812347, 819487, 877867, 1196857, 1229197, 1262617, 1279177
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+6, p+12 and p+16 are consecutive primes.

Examples

			67 is in the sequence since 67, 71 = 67 + 4, 73 = 67 + 6, 79 = 67 + 12 and 83 = 67 + 16 are consecutive primes.

Links

Crossrefs

Subsequence of A078850. - R. J. Mathar, Feb 11 2013
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {4,2,6,4} &][[;;, 1]] (* Amiram Eldar, Feb 21 2025 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 2 && p4 - p3 == 6 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078954 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,4).

Original entry on oeis.org

1597, 3907, 12097, 12907, 38317, 58897, 65827, 90007, 90187, 112237, 129277, 134077, 140407, 176317, 204427, 336757, 374977, 390097, 394717, 435637, 486667, 538147, 543997, 588937, 618577, 678637, 702337, 922627, 990277, 996157, 1086247, 1248337, 1326037, 1348537
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+10, p+12 and p+16 are consecutive primes.

Examples

			90007 is in the sequence since 90007, 90011 = 90007 + 4, 90017 = 90007 + 10, 90019 = 90007 + 12 and 90023 = 90007 + 16 are consecutive primes.

Links

Crossrefs

Subsequence of A078851. - R. J. Mathar, Feb 11 2013
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[85000]],5,1],Differences[#] == {4,6,2,4}&]][[1]] (* Harvey P. Dale, Sep 30 2012 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078955 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,6).

Original entry on oeis.org

19, 1279, 1609, 2539, 3529, 4639, 5839, 15259, 19069, 32359, 71329, 75979, 88789, 97369, 112909, 113149, 130639, 135589, 138559, 191449, 229759, 246919, 290659, 312199, 346429, 349369, 357649, 384469, 396619, 416389, 418339, 421699, 433249, 435559, 450799, 460969
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+10, p+12 and p+18 are consecutive primes.

Examples

			19 is in the sequence since 19, 23 = 19 + 4, 29 = 19 + 10, 31 = 19 + 12 and 37 = 19 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078851. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[40000]],5,1],Differences[#]=={4,6,2,6}&]][[1]]  (* Harvey P. Dale, Feb 03 2011 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 19 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078956 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).

Original entry on oeis.org

43, 163, 643, 1213, 2953, 4003, 7573, 11923, 14533, 25453, 26683, 26713, 29863, 41593, 48523, 61543, 68473, 150193, 151153, 172423, 206803, 227593, 290023, 302563, 338563, 343813, 346543, 428023, 527053, 529033, 540373, 547483, 551713, 570403, 577513, 622603, 628993
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+10, p+16 and p+18 are consecutive primes.
All terms == 13 (mod 30). - Robert Israel, Oct 17 2023

Examples

			43 is in the sequence since 43, 47 = 43 + 4, 53 = 43 + 10, 59 = 43 + 16 and 61 = 43 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078852. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.

Programs

  • Maple
    L:= [0$5]:
p:= 1: R:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  L:= [L[2],L[3],L[4],L[5],p];
  if L -~ L[1] = [0, 4, 10, 16, 18] then
    count:= count+1;
    R:= R, L[1];
  fi
od:
R; # Robert Israel, Oct 17 2023
  • Mathematica
    Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={4,6,6,2}&][[All,1]] (* Harvey P. Dale, Jan 23 2021 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078957 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,6).

Original entry on oeis.org

12637, 14737, 15787, 17467, 78787, 95257, 104707, 120997, 154057, 243517, 250027, 252877, 351037, 357667, 443227, 496477, 501187, 593497, 624787, 696607, 750787, 917827, 949957, 1003087, 1025257, 1104097, 1109887, 1260877, 1279657, 1457857, 1517917, 1565167, 1654717
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+4, p+10, p+16 and p+22 are consecutive primes.

Examples

			15787 is in the sequence since 15787, 15791 = 15787 + 4, 15797 = 15787 + 10, 15803 = 15787 + 16 and 15809 = 15787 + 22 are consecutive primes.

Links

Crossrefs

Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[10^5]],5,1],Differences[#]=={4,6,6,6}&][[All,1]] (* Harvey P. Dale, Jun 23 2019 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078958 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,4,6).

Original entry on oeis.org

1601, 3911, 12101, 14621, 32051, 68891, 122021, 191441, 258101, 259151, 276581, 278801, 305471, 347051, 390101, 394721, 418331, 419591, 421691, 470201, 482501, 509681, 678641, 683471, 832361, 844421, 914351, 929051, 977351, 997091, 1043831, 1074701, 1104731, 1224851
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+6, p+8, p+12 and p+18 are consecutive primes.

Examples

			3911 is in the sequence since 3911, 3917 = 3911 + 6, 3919 = 3911 + 8, 3923 = 3911 + 12 and 3929 = 3911 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078853. - R. J. Mathar, May 06 2017
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[82000]],5,1],Differences[#]=={6,2,4,6}&][[All,1]] (* Harvey P. Dale, Jul 09 2021 *)
  • 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 == 4 && p5 - p4 == 6, 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

A078959 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,4).

Original entry on oeis.org

23, 53, 263, 1283, 2333, 5843, 6563, 14543, 19373, 32363, 41603, 48473, 49193, 51413, 75983, 88793, 106853, 113153, 115763, 138563, 150203, 160073, 163973, 204353, 223823, 229763, 246923, 284723, 319673, 326993, 337853, 338153, 357653, 433253, 443153, 460073, 460973
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+18 are consecutive primes.

Examples

			53 is a term since 53, 59 = 53 + 6, 61 = 53 + 8, 67 = 53 + 14 and 71 = 53 + 18 are consecutive primes.

Links

Crossrefs

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

Programs

  • Mathematica
    l = {}; For[n = 1, n < 10^5, n++, If[Prime[n] + 6 == Prime[n + 1] \[And] Prime[n] + 8 == Prime[n + 2] \[And] Prime[n] + 14 == Prime[n + 3] \[And] Prime[n] + 18 == Prime[n + 4], AppendTo[l, Prime[n]]]]; l (* Jake Foster, Oct 27 2008 *)
Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,2,6,4} &][[;;, 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 == 2 && p4 - p3 == 6 && p5 - p4 == 4, 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

A078961 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,2,4).

Original entry on oeis.org

31, 1291, 1861, 1987, 2677, 4507, 5641, 7867, 13681, 17377, 24097, 35521, 42451, 44257, 55807, 80671, 88651, 88801, 93481, 110557, 113011, 113161, 118891, 134581, 155371, 163981, 198817, 221707, 234181, 266671, 269377, 284731, 290611, 313981, 331537, 332461, 344161
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+16 are consecutive primes.

Examples

			31 is a term since 31, 37 = 31 + 6, 41 = 31 + 10, 43 = 31 + 12 and 47 = 31 + 16 are consecutive primes.

Links

Crossrefs

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

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[26000]],5,1],Differences[#]=={6,4,2,4}&]][[1]] (* Harvey P. Dale, Aug 26 2014 *)
  • 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 == 4, 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
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