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

A101995 Primes of the form 4*k-1 such that 8*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.

Original entry on oeis.org

179, 53639, 63419, 126839, 127139, 254279, 296099, 340919, 607319, 810539, 1069199, 1122659, 1598699, 1621619, 1820999, 1866239, 1912679, 1920959, 2045339, 2138399, 2157899, 2245319, 2278079, 2357219, 2667779, 2865839
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 179 is a term.

Links

Crossrefs

Cf. A002515, A101794.
Cf. A101994, A101996, A101997, A101998, A101999.
Subsequence of A002145, A101791 and A101795.

Programs

  • Mathematica
    4 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 6]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)
  • 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) && isprime(64*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 4*A101994(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

A101797 Primes of the form 16*k-1 such that 4*k-1, 8*k-1 and 32*k-1 are also primes.

Original entry on oeis.org

719, 1439, 10799, 14159, 48479, 68639, 109919, 214559, 231359, 253679, 285599, 298799, 329999, 350159, 405599, 429119, 430799, 451679, 488399, 491279, 507359, 508559, 533999, 557759, 666959, 671039, 918959, 1014719, 1017119, 1148879
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 719 is a term.

Links

Crossrefs

Cf. A002515, A101794, A101795, A101796, A101798.
Subsequence of A127576 and A101793.
Subsequence: A101997.

Programs

  • Mathematica
    16#-1&/@Select[Range[80000],AllTrue[#*2^Range[2,5]-1,PrimeQ]&] (* Harvey P. Dale, Apr 25 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) && isprime(32*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 16*A101794(n) - 1 = 4*A101795(n) + 3 = 2*A101796(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

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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