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 1-7 of 7 results.

A101994 Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1 and 64*k-1 are all primes.

Original entry on oeis.org

45, 13410, 15855, 31710, 31785, 63570, 74025, 85230, 151830, 202635, 267300, 280665, 399675, 405405, 455250, 466560, 478170, 480240, 511335, 534600, 539475, 561330, 569520, 589305, 666945, 716460, 743160, 748215, 766785, 799350, 860835
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 45 is a term.

Links

Crossrefs

Cf. A002515, A101995, A101996, A101997, A101998, A101999.
Subsequence of A005099, A005122, A101790 and A101794.

Programs

  • Mathematica
    Select[Range[10^6], And @@ PrimeQ[2^Range[2, 6]*# - 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) && isprime(64*k-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

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

A101998 Primes of the form 32*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 64*k-1 are also primes.

Original entry on oeis.org

1439, 429119, 507359, 1014719, 1017119, 2034239, 2368799, 2727359, 4858559, 6484319, 8553599, 8981279, 12789599, 12972959, 14567999, 14929919, 15301439, 15367679, 16362719, 17107199, 17263199, 17962559, 18224639, 18857759
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 1439 is a term.

Links

Crossrefs

Cf. A101994, A101995, A101996, A101997, A101999.
Subsequence of A127578 and A101798.

Programs

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

Formula

a(n) = 32*A101994(n) - 1 = 8*A101995(n) + 7 = 4*A101996(n) + 3 = 2*A101997(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

A101999 Primes of the form 64*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 32*k-1 are also primes.

Original entry on oeis.org

2879, 858239, 1014719, 2029439, 2034239, 4068479, 4737599, 5454719, 9717119, 12968639, 17107199, 17962559, 25579199, 25945919, 29135999, 29859839, 30602879, 30735359, 32725439, 34214399, 34526399, 35925119, 36449279
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 2879 is a term.

Links

Crossrefs

Cf. A101994, A101995, A101996, A101997, A101998.
Subsequence of A127579.

Programs

  • Mathematica
    64#-1&/@Select[Range[570000],AllTrue[#*2^Range[2,6]-1,PrimeQ]&] (* Harvey P. Dale, Aug 07 2021 *)
  • PARI
    is(k) = if(k % 64 == 63, my(m = k\64 + 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) = 64*A101994(n) - 1 = 16*A101995(n) + 15 = 8*A101996(n) + 7 = 4*A101997(n) + 3 = 2*A101998(n) + 1. - Amiram Eldar, May 13 2024
Showing 1-7 of 7 results.

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

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