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 1-4 of 4 results.

A023304 Primes that remain prime through 4 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

13, 31, 181, 541, 661, 1087, 1861, 2179, 2719, 3727, 7459, 8089, 8707, 9109, 10639, 17341, 19333, 22501, 23293, 29287, 32797, 39847, 40387, 42703, 46591, 51613, 53101, 56149, 56809, 57829, 59233, 80779, 87643, 89113, 89413, 91291, 93979, 94261, 98899
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 2*p+5, 4*p+15, 8*p+35 and 16*p+75 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023205, A023243, A023274, and A089038.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35) and IsPrime(16*n+75)]; // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 5 &, #, 4] > 0 &] (* Michael De Vlieger, Sep 27 2016 *)
Select[Prime[Range[10000]],AllTrue[Rest[NestList[2#+5&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2020 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 27 2016

Extensions

Definition clarified by Harvey P. Dale, Oct 23 2020

A023332 Primes that remain prime through 5 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

13, 541, 1087, 1861, 3727, 23293, 40387, 87643, 98899, 109111, 115153, 116329, 119101, 131617, 133597, 163909, 197521, 214021, 215389, 218227, 238207, 263239, 294751, 489901, 493693, 665527, 734131, 767881, 808693, 895351, 1038127, 1051957
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 2*p+5, 4*p+15, 8*p+35, 16*p+75 and 32*p+155 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023205, A023243, A023274, A023304, and A089038.

Programs

  • Magma
    [n: n in [1..5000000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35) and IsPrime(16*n+75) and IsPrime(32*n+155)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    txQ[p_]:=AllTrue[NestList[2#+5&,p,5],PrimeQ]; Select[Prime[Range[83000]],txQ] (* Harvey P. Dale, May 10 2024 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Oct 09 2016

A129932 Prime numbers p such that p remains prime through 6 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

541, 1861, 109111, 119101, 131617, 895351, 1774447, 2343037, 2906623, 3686743, 3686953, 4330783, 4594309, 4921129, 4922329, 5495989, 5654137, 6712591, 7093057, 7729537, 9188623, 9842263, 10492297, 10991983, 11270671, 12307453
Offset: 1

Views

Author

Ray G. Opao, Jun 06 2007

Keywords

Links

Crossrefs

Cf. A023332, A023304, A023274, A023243.

Programs

  • Mathematica
    fQ[n_] := Union[PrimeQ /@ NestList[2 # + 5 &, n, 6]] == {True}; lst = {}; Do[ p = Prime@n; If[fQ@p, Print@p; AppendTo[lst, p]], {n, 10^7}]; lst (* Robert G. Wilson v *)
Select[Prime[Range[810000]],AllTrue[Rest[NestList[2#+5&,#,6]],PrimeQ]&] (* Harvey P. Dale, Mar 03 2025 *)

Extensions

More terms from Robert G. Wilson v, Jun 06 2007
Definition clarified by Harvey P. Dale, Mar 03 2025

A129931 Numbers n such that n remains prime through 7 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

4594309, 4921129, 5495989, 7093057, 14722021, 23008891, 23380471, 24251167, 24296563, 49201981, 51788797, 62123011, 64649503, 69326779, 78274321, 88022797, 95575771, 100099267, 125796127, 128185777, 129299011, 130858711
Offset: 1

Views

Author

Ray G. Opao, Jun 06 2007

Keywords

Crossrefs

Cf. A023243, A023274, A023304, A023332.

Programs

  • Mathematica
    fQ[n_] := Union[PrimeQ /@ NestList[2 # + 5 &, n, 7]] == {True}; lst = {}; Do[ p = Prime@n; If[fQ@p, Print@p; AppendTo[lst, p]], {n, 10^7}]; lst (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Jun 06 2007
Showing 1-4 of 4 results.

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

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