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 1-6 of 6 results.

A101794 Numbers k such that 4*k-1, 8*k-1, 16*k-1 and 32*k-1 are all primes.

Original entry on oeis.org

45, 90, 675, 885, 3030, 4290, 6870, 13410, 14460, 15855, 17850, 18675, 20625, 21885, 25350, 26820, 26925, 28230, 30525, 30705, 31710, 31785, 33375, 34860, 41685, 41940, 57435, 63420, 63570, 71805, 74025, 78585, 83865, 85230, 93075
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 45 is a term.

Links

Crossrefs

Cf. A002515, A101795, A101796, A101797, A101798.
Subsequence of A005099, A005122 and A101790.
Subsequence: A101994.

Programs

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

A101997 Primes of the form 16*k-1 such that 4*k-1, 8*k-1, 32*k-1 and 64*k-1 are also primes.

Original entry on oeis.org

719, 214559, 253679, 507359, 508559, 1017119, 1184399, 1363679, 2429279, 3242159, 4276799, 4490639, 6394799, 6486479, 7283999, 7464959, 7650719, 7683839, 8181359, 8553599, 8631599, 8981279, 9112319, 9428879, 10671119
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 719 is a term.

Links

Crossrefs

Cf. A101994, A101995, A101996, A101998, A101999.
Subsequence of A127576, A101793 and A101797.

Programs

  • Mathematica
    Select[With[{c=2^Range[2,6]},Table[c n-1,{n,700000}]],AllTrue[#,PrimeQ]&][[All,3]] (* Harvey P. Dale, Nov 29 2018 *)
  • PARI
    is(k) = if(k % 16 == 15, my(m = k\16 + 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) = 16*A101994(n) - 1 = 4*A101995(n) + 3 = 2*A101996(n) + 1. - Amiram Eldar, May 13 2024

A101795 Primes of the form 4*k-1 such that 8*k-1, 16*k-1 and 32*k-1 are also primes.

Original entry on oeis.org

179, 359, 2699, 3539, 12119, 17159, 27479, 53639, 57839, 63419, 71399, 74699, 82499, 87539, 101399, 107279, 107699, 112919, 122099, 122819, 126839, 127139, 133499, 139439, 166739, 167759, 229739, 253679, 254279, 287219, 296099
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 179 is a term.

Links

Crossrefs

Cf. A002515, A101794, A101796, A101797, A101798.
Subsequence of A002145 and A101791.
Subsequence: A101995.

Programs

  • Mathematica
    Select[Table[4n-1,{n,75000}],AllTrue[(#+1)*{1,2,4,8}-1,PrimeQ]&] (* Harvey P. Dale, Apr 23 2019 *)
  • PARI
    is(k) = if(k % 4 == 3, my(m = k\4 + 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) = 4*A101794(n) - 1. - Amiram Eldar, May 13 2024

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

A101798 Primes of the form 32*k-1 such that 4*k-1, 8*k-1 and 16*k-1 are also primes.

Original entry on oeis.org

1439, 2879, 21599, 28319, 96959, 137279, 219839, 429119, 462719, 507359, 571199, 597599, 659999, 700319, 811199, 858239, 861599, 903359, 976799, 982559, 1014719, 1017119, 1067999, 1115519, 1333919, 1342079, 1837919, 2029439, 2034239
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 1439 is a term.

Links

Crossrefs

Cf. A002515, A101794, A101795, A101796, A101797.
Subsequence of A127578.
Subsequence: A101998.

Programs

  • Mathematica
    32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)
Select[Prime[Range[200000]],Mod[#,32]==31&&AllTrue[{4,8,16} (#+1)/32-1,PrimeQ]&] (* Harvey P. Dale, Feb 20 2025 *)
  • PARI
    is(k) = if(k % 32 == 31, my(m = k\32 + 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) = 32*A101794(n) - 1 = 8*A101795(n) + 7 = 4*A101796(n) + 3 = 2*A101797(n) + 1. - Amiram Eldar, May 13 2024
Showing 1-6 of 6 results.

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