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 1-5 of 5 results.

A137869 Primes p with property that (p - previous prime) >= 6 and (next prime - p) >= 6.

Original entry on oeis.org

53, 89, 157, 173, 211, 251, 257, 263, 293, 331, 337, 359, 367, 373, 389, 409, 449, 479, 509, 541, 547, 557, 563, 577, 587, 593, 607, 631, 653, 683, 691, 701, 709, 719, 727, 733, 751, 787, 797, 839, 919, 929, 947, 953, 977, 983, 991, 997, 1039, 1069, 1103, 1109, 1117
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 29 2008

Keywords

Links

Crossrefs

These are the primes not in A167773.
Cf. A053070.

Programs

  • Magma
    [p:p in PrimesInInterval(3,1200)|p-PreviousPrime(p) ge 6 and NextPrime(p)-p ge 6]; // Marius A. Burtea, Aug 11 2019
  • Maple
    M:=1000; t1:=[];
for i from 2 to M do
p:=ithprime(i); o:=prevprime(p); q:=nextprime(p);
if p-o >= 6 and q-p >= 6 then t1:=[op(t1),p]; fi; od:
t1; # N. J. A. Sloane
  • Mathematica
    lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 20 2009 *)
Select[Partition[Prime[Range[200]],3,1],Min[Differences[#]]>5&][[;;,2]] (* Harvey P. Dale, Oct 29 2023 *)
  • PARI
    p=q=2;forprime(r=2,999,r-q>4 & q-p>4 & print1(q","); p=q; q=r) \\ M. F. Hasler, May 02 2009

Extensions

Edits and more terms from N. J. A. Sloane, May 02 2009

A141296 Primes p such that p-6^2, p-6, p, p+6 and p+6^2 are consecutive primes.

Original entry on oeis.org

846493, 1407187, 1427963, 3675277, 3750833, 4266673, 4331647, 4346767, 4348307, 4841693, 5952077, 6827237, 7421137, 7470143, 7684483, 7974143, 8569153, 8651543, 8976713, 9073783, 9552083, 11245763, 11459317, 12348997, 12524503
Offset: 1

Views

Author

Rick L. Shepherd, Jun 24 2008

Keywords

Comments

Equivalently, third of five consecutive primes with this consecutive difference pattern: 30, 6, 6, 30. Subsequence of A141279.

Examples

			a(1) = 846493 because 846457, 846487, 846493, 846499 and 846529 are consecutive primes and no smaller primes have this pattern of differences.

Links

Crossrefs

Cf. A141279, A053070.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[830000]],5,1],Differences[#] == {30,6,6,30}&]] [[3]] (* Harvey P. Dale, Sep 09 2011 *)

A167773 Primes p with property that (p-previous prime) < 6 or (next prime-p) < 6.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 241, 269, 271, 277, 281, 283, 307, 311, 313, 317, 347
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 11 2009

Keywords

Crossrefs

These are the primes not in A137869.
Cf. A053070.

Programs

  • Mathematica
    Join[{2},Select[Partition[Prime[Range[100]],3,1],#[[2]]-#[[1]]<6||#[[3]]-#[[2]]<6&][[;;,2]]] (* Harvey P. Dale, Oct 29 2023 *)

Extensions

Corrected (43 inserted) by R. J. Mathar, May 30 2010
Definition corrected to match data. - Harvey P. Dale_, Oct 29 2023

A178135 Balanced primes separated from the next lower and next higher prime neighbors by 54.

Original entry on oeis.org

6314447, 7855163, 9715103, 10133467, 10851497, 12820427, 13442537, 14064317, 14172007, 15945437, 18715547, 20208163, 21488263, 22916767, 23924827, 24079357, 25660883, 27099283, 27245627, 27613093, 29162977, 31215643
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 20 2010

Keywords

Crossrefs

Cf. A006562, A053070, A053072, A053073, A053074, A053075, A053076, A053077, A053078

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[p-Prime[n-1]==Prime[n+1]-p==6*9,AppendTo[lst,p]],{n,9!,10!}];lst
Select[Partition[Prime[Range[2*10^6]],3,1],Differences[#]=={54,54}&][[All,2]] (* Harvey P. Dale, Jul 07 2020 *)

A178136 Balanced primes separated from the next lower and next higher prime neighbors by 60.

Original entry on oeis.org

4911311, 5309599, 9113323, 11355857, 11397163, 13940117, 14306263, 14313587, 14585149, 17172581, 21126169, 24419341, 24581863, 24861691, 24922351, 25308859, 26241811, 26722583, 27408253, 28740979, 29675197, 30045871
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 20 2010

Keywords

Crossrefs

Cf. A006562, A053070, A053072, A053073, A053074, A053075, A053076, A053077, A053078, A178135

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[p-Prime[n-1]==Prime[n+1]-p==6*10,AppendTo[lst,p]],{n,8!,2*10!}];lst
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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