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.

A023272 Primes that remain prime through 3 iterations of the function f(x) = 2*x + 1.

Original entry on oeis.org

2, 5, 89, 179, 359, 509, 1229, 1409, 2699, 3539, 6449, 10589, 11549, 11909, 12119, 17159, 19709, 19889, 22349, 26189, 27479, 30389, 43649, 53639, 53849, 55229, 57839, 60149, 61409, 63419, 66749, 71399, 74699, 75329, 82499, 87539, 98369, 101399, 104369
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 2*p+1, 4*p+3 and 8*p+7 are also primes. - Vincenzo Librandi, Aug 04 2010
For n > 2, a(n) == 29 (mod 30). - Zak Seidov, Jan 31 2013

Links

Crossrefs

Intersection of A007700 and A023231.
Cf. A005384, A005385, A023302, A023330, A057331, A005602.

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(4*n+3) and IsPrime(8*n+7)] // Vincenzo Librandi, Aug 04 2010
  • Maple
    p:=2: for n from 1 to 5000 do if(isprime(2*p+1) and isprime(4*p+3) and isprime(8*p+7))then printf("%d, ",p): fi: p:=nextprime(p): od: # Nathaniel Johnston, Jun 30 2011
  • Mathematica
    Select[Prime[Range[10^3*4]], PrimeQ[a1=2*#+1] && PrimeQ[a2=2*a1+1] && PrimeQ[a3=2*a2+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
Join[{2, 5}, Select[Range[89, 104369, 30], PrimeQ[#] && PrimeQ[2*# + 1] && PrimeQ[4*# + 3] && PrimeQ[8*# + 7] &]] (* Zak Seidov, Jan 31 2013 *)
p3iQ[n_]:=AllTrue[NestList[2#+1&,n,3],PrimeQ]; Join[{2,5},Select[ Range[ 89,200000,30],p3iQ]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2019 *)
  • PARI
    is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3)&&isprime(8*n+7) \\ Charles R Greathouse IV, Mar 21 2013

A023294 Primes that remain prime through 3 iterations of function f(x) = 8x + 7.

Original entry on oeis.org

659, 2549, 5189, 6269, 7229, 7949, 9209, 11579, 16139, 18089, 22739, 25589, 26099, 26339, 29009, 30689, 40289, 51719, 55799, 59669, 60689, 61379, 63599, 69959, 70229, 74609, 85829, 94949, 95819, 102539, 109589, 118169, 121469, 135599, 136889
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+7, 64*p+63 and 512*p+511 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023231, A023263, and A139487.

Programs

  • Magma
    [n: n in [1..450000] | IsPrime(n) and IsPrime(8*n+7) and IsPrime(64*n+63) and IsPrime(512*n+511)]; // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 29 (mod 30). - John Cerkan, Sep 23 2016

A023322 Primes that remain prime through 4 iterations of function f(x) = 8x + 7.

Original entry on oeis.org

7949, 25589, 55799, 61379, 69959, 70229, 74609, 174569, 188369, 204719, 220469, 225629, 233759, 250919, 286619, 363659, 552749, 592139, 658349, 735419, 783269, 827549, 931949, 1018889, 1065839, 1126319, 1132739, 1187939, 1215629, 1378529
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+7, 64*p+63, 512*p+511 and 4096*p+4095 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023231, A023263, A023294, and A139487.

Programs

  • Magma
    [n: n in [1..5000000] | IsPrime(n) and IsPrime(8*n+7) and IsPrime(64*n+63) and IsPrime(512*n+511) and IsPrime(4096*n+4095)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    rp4Q[p_]:=AllTrue[Rest[NestList[8#+7&,p,4]],PrimeQ]; Select[Prime[Range[110000]],rp4Q] (* Harvey P. Dale, Aug 03 2023 *)

Formula

a(n) == 9 (mod 10). - John Cerkan, Oct 08 2016

A023350 Primes that remain prime through 5 iterations of function f(x) = 8x + 7.

Original entry on oeis.org

25589, 220469, 225629, 286619, 783269, 1215629, 1407389, 1542029, 1642919, 2329469, 2776979, 3104159, 4082759, 4229129, 5405999, 5905619, 6548849, 6862859, 7681409, 7904669, 8623799, 8971049, 9599309, 9658469, 9725039, 11420579
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+7, 64*p+63, 512*p+511, 4096*p+4095 and 32768*p+32767 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023231, A023263, A023294, A023322, and A139487.

Programs

  • Magma
    [n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+7) and IsPrime(64*n+63) and IsPrime(512*n+511) and IsPrime(4096*n+4095) and IsPrime(32768*n+32767)]; // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    i5Q[p_]:=AllTrue[Rest[NestList[8#+7&,p,5]],PrimeQ]; Select[Prime[Range[760000]],i5Q] (* Harvey P. Dale, Jul 05 2025 *)

Formula

a(n) == 29 (mod 30). - John Cerkan, Nov 08 2016

A158238 Primes p such that (p-7)/8 and 8p + 7 are both prime.

Original entry on oeis.org

23, 47, 863, 1103, 1439, 1583, 1823, 2879, 3359, 4943, 5279, 6719, 7823, 8783, 9743, 11279, 11903, 12479, 13103, 16703, 18719, 19583, 20399, 20879, 21503, 23279, 23663, 25343, 26399, 27743, 29759, 33119, 35279, 38303, 39359, 39503, 41183
Offset: 1

Views

Author

Zak Seidov, Mar 14 2009

Keywords

Links

Crossrefs

Cf. A023231 Numbers n such that n and 8n + 7 are both prime.

Programs

  • Mathematica
    Select[Prime[Range[5000]],AllTrue[{(#-7)/8,8#+7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 24 2015 *)
  • PARI
    isok(p) = isprime(p) && isprime(8*p+7) && ((p % 8)==7) && isprime((p-7)/8); \\ Michel Marcus, Oct 16 2013

Formula

23, (23-7)/8=2, and 8*23+7=191 are all prime.
Showing 1-5 of 5 results.

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

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