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.

A101790 Numbers k such that 4*k-1, 8*k-1 and 16*k-1 are all primes.

Original entry on oeis.org

3, 45, 90, 180, 255, 258, 363, 378, 453, 483, 615, 675, 705, 873, 885, 978, 1350, 1533, 1770, 1788, 2673, 2793, 2868, 3030, 3225, 3240, 4203, 4290, 4548, 4830, 4998, 5103, 5253, 5295, 5568, 5775, 5955, 6060, 6138, 6870, 7383, 7713, 8133, 8370, 8580, 9000
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Keywords

Examples

			4*3 - 1 = 11, 8*3 - 1 = 23 and 16*3 - 1 = 47 are primes, so 3 is a term.

Links

Crossrefs

Cf. A002515, A101791, A101792, A101793.
Subsequence of A005099 and A005122.
Subsequences: A101794, A101994.

Programs

  • Magma
    [n: n in [0..10000] | IsPrime(4*n-1) and IsPrime(8*n-1) and IsPrime(16*n-1)]; // Vincenzo Librandi, Nov 17 2010
  • Mathematica
    Select[Range[10^4], And @@ PrimeQ[2^Range[2, 4]*# - 1] &] (* Amiram Eldar, May 12 2024 *)
  • PARI
    is(k) = isprime(4*k-1) && isprime(8*k-1) && isprime(16*k-1); \\ Amiram Eldar, May 12 2024

A101793 Primes of the form 16*k-1 such that 4*k-1 and 8*k-1 are also primes.

Original entry on oeis.org

47, 719, 1439, 2879, 4079, 4127, 5807, 6047, 7247, 7727, 9839, 10799, 11279, 13967, 14159, 15647, 21599, 24527, 28319, 28607, 42767, 44687, 45887, 48479, 51599, 51839, 67247, 68639, 72767, 77279, 79967, 81647, 84047, 84719, 89087, 92399, 95279, 96959, 98207
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Keywords

Examples

			4*3-1 = 11, 8*3-1 = 23 and 16*3-1 = 47 are primes, so 47 is a term.

Links

Crossrefs

Cf. A002515, A101790, A101791, A101792.
Subsequence of A127576.
Subsequences: A101797, A101997.

Programs

  • Mathematica
    16#-1&/@Select[Range[10000],AllTrue[{4#-1,8#-1,16#-1},PrimeQ]&] (* Harvey P. Dale, Jun 13 2015 *)
  • PARI
    is(k) = if(k % 16 == 15, my(m = k\16 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 16*A101790(n) - 1 = 4*A101791(n) + 3 = 2*A101792(n) + 1. - Amiram Eldar, May 13 2024

A101996 Primes of the form 8*k-1 such that 4*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.

Original entry on oeis.org

359, 107279, 126839, 253679, 254279, 508559, 592199, 681839, 1214639, 1621079, 2138399, 2245319, 3197399, 3243239, 3641999, 3732479, 3825359, 3841919, 4090679, 4276799, 4315799, 4490639, 4556159, 4714439, 5335559, 5731679
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004

Keywords

Examples

			4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 359 is a term.

Links

Crossrefs

Cf. A101789, A101994, A101995, A101997, A101998, A101999.
Subsequence of A007522, A101792 and A101796.

Programs

  • Mathematica
    8#-1&/@Select[Range[720000],AllTrue[{4,8,16,32,64}#-1,PrimeQ]&] (* Harvey P. Dale, Jan 17 2023 *)
Select[Table[2^Range[2,6] n-1,{n,750000}],AllTrue[#,PrimeQ]&][[;;,2]] (* Harvey P. Dale, Jun 03 2023 *)
  • PARI
    is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1) && isprime(64*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 8*A101994(n) - 1 = 2*A101995(n) + 1. - Amiram Eldar, May 13 2024

Extensions

Corrected by T. D. Noe, Nov 15 2006

A101796 Primes of the form 8*k-1 such that 4*k-1, 16*k-1 and 32*k-1 are also primes.

Original entry on oeis.org

359, 719, 5399, 7079, 24239, 34319, 54959, 107279, 115679, 126839, 142799, 149399, 164999, 175079, 202799, 214559, 215399, 225839, 244199, 245639, 253679, 254279, 266999, 278879, 333479, 335519, 459479, 507359, 508559
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Keywords

Examples

			4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 359 is a term.

Links

Crossrefs

Cf. A002515, A101794, A101795, A101797, A101798.
Subsequence of A007522 and A101792.
Subsequence: A101996.

Programs

  • Mathematica
    8 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)
  • PARI
    is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 8*A101794(n) - 1 = 2*A101795(n) + 1. - Amiram Eldar, May 13 2024

A101791 Primes of the form 4*k-1 such that 8*k-1 and 16*k-1 are also primes.

Original entry on oeis.org

11, 179, 359, 719, 1019, 1031, 1451, 1511, 1811, 1931, 2459, 2699, 2819, 3491, 3539, 3911, 5399, 6131, 7079, 7151, 10691, 11171, 11471, 12119, 12899, 12959, 16811, 17159, 18191, 19319, 19991, 20411, 21011, 21179, 22271, 23099, 23819
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Keywords

Examples

			4*3-1 = 11, 8*3-1 = 23 and 16*3-1 = 47 are primes, so 11 is a term.

Links

Crossrefs

Cf. A002515, A101790, A101792, A101793.
Subsequence of A002145.
Subsequences: A101795, A101995.

Programs

  • Mathematica
    p4816Q[n_]:=Module[{nn=(n+1)/4},And@@PrimeQ[{n,8nn-1,16nn-1}]]; Select[ 4*Range[6000]-1,p4816Q] (* Harvey P. Dale, Nov 25 2011 *)
  • PARI
    is(k) = if(k % 4 == 3, my(m = k\4 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 4*A101790(n) - 1. - Amiram Eldar, May 13 2024
Showing 1-5 of 5 results.

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