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 1-10 of 21 results. Next

A078946 Primes p such that p, p+2, p+6, p+12 and p+14 are consecutive primes.

Original entry on oeis.org

17, 227, 1277, 1607, 3527, 3917, 4637, 4787, 27737, 38447, 39227, 44267, 71327, 97367, 99707, 113147, 122027, 122387, 124337, 165707, 183497, 187127, 191447, 197957, 198827, 275447, 290657, 312197, 317957, 347057, 349397, 416387, 418337, 421697, 427067, 443867
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Examples

			227 is in the sequence since 227, 229 = 227 + 2, 233 = 227 + 6, 239 = 227 + 12 and 241 = 227 + 14 are consecutive primes.

Links

Crossrefs

Subsequence of A128468.
Subsequence of A078847. - R. J. Mathar, Feb 10 2013
Cf. A001223, A078866, A078867, A078947-A078971, A022006, A022007.

Programs

  • Magma
    [p: p in PrimesInInterval(7,1000000) | forall{i: i in [2,6,12,14] | IsPrime(p+i)}]; // Vincenzo Librandi, Apr 19 2015
  • Mathematica
    Rest@ Select[Prime@ Range@ 36000, AllTrue[{2, 6, 12, 14} + #, PrimeQ] &] (* Michael De Vlieger, Apr 18 2015, Version 10 *)
Select[Partition[Prime[Range[36000]],5,1],Differences[#]=={2,4,6,2}&][[All,1]] (* Harvey P. Dale, Jun 14 2022 *)
  • PARI
    isok(p) = isprime(p) && (nextprime(p+1)==p+2) && (nextprime(p+3)== p+6) && (nextprime(p+7)==p+12) && (nextprime(p+13)==p+14); \\ Michel Marcus, Dec 10 2013
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 17 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078969 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,6,4).

Original entry on oeis.org

3301, 15901, 18211, 30091, 53611, 71341, 77551, 80911, 89101, 120811, 252151, 285451, 292471, 294781, 344251, 601801, 616501, 744811, 792691, 809821, 908521, 912391, 1152631, 1154221, 1279801, 1376491, 1398031, 1455361, 1464271, 1500511, 1503031, 1555111, 1594261
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+22 are consecutive primes.

Examples

			30091 is in the sequence since 30091, 30097 = 30091 + 6, 30103 = 30091 + 12, 30109 = 30091 + 18 and 30113 = 30091 + 22 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[#] == {6,6,6,4} &][[;;, 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 == 6 && p4 - p3 == 6 && p5 - p4 == 4, 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

A078947 Primes p such that the differences between the 5 consecutive primes starting with p are (2,4,6,6).

Original entry on oeis.org

41, 641, 1091, 4001, 9461, 26681, 26711, 44531, 79811, 103991, 110921, 112571, 172421, 223241, 276821, 289841, 290021, 317771, 373181, 381371, 434921, 450881, 493121, 602081, 678761, 788351, 834131, 907211, 974861, 1076501, 1081121, 1097891, 1200371, 1409531, 1426151
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+2, p+6, p+12 and p+18 are consecutive primes.

Examples

			641 is in the sequence since 641, 643 = 641 + 2, 647 = 641 + 6, 653 = 641 + 12 and 659 = 641 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078847.
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 4, 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 == 4 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 11 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078948 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,2).

Original entry on oeis.org

29, 59, 269, 1289, 2129, 2789, 5639, 8999, 13679, 14549, 18119, 36779, 62129, 75989, 80669, 83219, 88799, 93479, 113159, 115769, 124769, 132749, 150209, 160079, 163979, 203309, 207509, 223829, 228509, 278489, 282089, 284729, 298679, 312929, 313979, 323369, 337859
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+2, p+8, p+12 and p+14 are consecutive primes.
All terms are congruent to 29 (mod 30). - Muniru A Asiru, Sep 04 2017

Examples

			59 is in the sequence since 59, 61 = 59 + 2, 67 = 59 + 8, 71 = 59 + 12 and 73 = 59 + 14 are consecutive primes.

Links

Crossrefs

Subsequence of A078848. - R. J. Mathar, Feb 10 2013
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • GAP
    K:=26*10^7+1;; # to get all terms <= K.
P:=Filtered([1,3..K],IsPrime);;  I:=[2,6,4,2];;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
Q:=List(Positions(List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]),I),i->P[i]); # Muniru A Asiru, Sep 04 2017
  • Maple
    for i from 1 to 10^5 do if [ithprime(i+1),ithprime(i+2),ithprime(i+3),ithprime(i+4)] = [ithprime(i)+2,ithprime(i)+8,ithprime(i)+12,ithprime(i)+14] then print(ithprime(i)); fi; od;  # Muniru A Asiru, Sep 04 2017
  • Mathematica
    Select[Partition[Prime[Range[26000]],5,1],Differences[#]=={2,6,4,2}&][[;;,1]] (* Harvey P. Dale, Dec 10 2024 *)
  • 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 == 4 && 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

A078949 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,6).

Original entry on oeis.org

71, 431, 2339, 2381, 5849, 6959, 27791, 32561, 41609, 45119, 46439, 48479, 51419, 54401, 63599, 78779, 81551, 106859, 115319, 130631, 138569, 143501, 153269, 166601, 183569, 196169, 204359, 229751, 246929, 266081, 279119, 321311, 326999, 350729, 357659, 362741
Offset: 1

Views

Author

Labos Elemer, Dec 19 2002

Keywords

Comments

Equivalently, primes p such that p, p+2, p+8, p+12 and p+18 are consecutive primes.

Examples

			71 is in the sequence since 71, 73 = 71 + 2, 79 = 71 + 8, 83 = 71 + 12 and 89 = 71 + 18 are consecutive primes.

Links

Crossrefs

Subsequence of A078848. - R. J. Mathar, Feb 10 2013
Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 4, 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 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

From Amiram Eldar, Feb 21 2025: (Start)
a(n) == 5 (mod 6).
a(n) == 11 or 29 (mod 30). (End)

Extensions

Edited by Dean Hickerson, Dec 20 2002

A078950 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,6,4).

Original entry on oeis.org

149, 599, 27059, 31319, 42179, 65699, 75209, 85829, 87539, 92219, 135599, 170759, 205949, 221069, 249419, 274829, 278609, 280589, 287849, 302579, 307259, 308309, 350429, 355499, 398339, 406499, 416399, 422549, 541529, 566549, 573479, 585839, 603899, 609599, 637709
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+18 are consecutive primes.

Examples

			149 is in the sequence since 149, 151 = 149 + 2, 157 = 149 + 8, 163 = 149 + 14 and 167 = 149 + 18 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, 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 == 2 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 4, 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

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
Showing 1-10 of 21 results. Next

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