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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A138660 Primes p such that (12*p - 1, 12*p + 1) and (18*p - 1, 18*p + 1) are twin primes.

Original entry on oeis.org

29, 1051, 6719, 9059, 10501, 27749, 27791, 36749, 51421, 83761, 86729, 108751, 115249, 120049, 124139, 124529, 138629, 148861, 152839, 162091, 169009, 176609, 178249, 178921, 202481, 203141, 209621, 228199, 232681, 244411, 302779, 309259
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Keywords

Examples

			29 is a term since it is a prime and (12*29 - 1, 12*29 + 1) = (347, 349) and (18*29 - 1, 18*29 + 1) = (521, 523) are twin primes.
1051 is a term since it is a prime and (12*1051 - 1, 12*1051+ 1) = (12611, 12613) and (18*1051 - 1, 18*1051 + 1) = (18917, 18919) are twin primes.

Links

Crossrefs

Intersection of A138242 and A138248.
Cf. A001097, A001359, A006512.

Programs

  • Magma
    [p: p in PrimesUpTo(100000)| IsPrime(12*p-1) and IsPrime(12*p+1) and IsPrime(18*p-1) and IsPrime(18*p+1)]; // Vincenzo Librandi, Nov 24 2010
  • Mathematica
    a=12;b=18;Select[Prime[Range[14^4]],PrimeQ[a*#-1]&&PrimeQ[a*#+1]&&PrimeQ[b*#-1]&&PrimeQ[b*#+1]&]
Select[Prime[Range[30000]],AllTrue[{12#-1,12#+1,18#-1,18#+1},PrimeQ]&] (* Harvey P. Dale, Dec 31 2024 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010

A317029 Invertible primes p such that k*p - 1 and k*p + 1 is a twin prime pair; for k = 12.

Original entry on oeis.org

19, 601, 1601, 16661, 16981, 19609, 60689, 66809, 69001, 69011, 100169, 119191, 189901, 196919, 616961, 1061689, 1088089, 1091119, 1106069, 1196089, 1198069, 1611601, 1666019, 1688969, 1800119, 1861889, 1891619, 1891661, 1910669, 1996681, 6060091, 6160601, 6196909
Offset: 1

Views

Author

K. D. Bajpai, Jul 19 2018

Keywords

Comments

Intersection of A048890 (invertible primes) and A138242.
k = 12 is the smallest integer to produce such sequence.

Examples

			a(2) = 601 is an invertible prime; 12*601 - 1 = 7211; 12*601 + 1 = 7213; 7211 and 7213 form a twin prime pair.
a(4) = 16661 is an invertible prime; 12*16661 - 1 = 199931; 12*16661 + 1 = 199933; 199931 and 199933 form a twin prime pair.

Crossrefs

Cf. A048890, A001359, A006512, A124519, A138242.

Programs

  • Mathematica
    k = 12; Select[lst = {};
fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, rid = Reverse[id /. {6 -> 9, 9 -> 6}];Union@Join[id, allset] == allset && PrimeQ@FromDigits@rid && rid != id];Do[If[PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 12000000}]; lst,
PrimeQ[k# + 1] && PrimeQ[k# - 1] &]
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