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 1-9 of 9 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

A124516 a(n) = least k such that 2^i*k-1 is prime for 1<=i<=n.

Original entry on oeis.org

2, 2, 3, 3, 45, 45, 561330, 9549960, 42932385, 13044904290, 277344139215, 277344139215, 2045466215756535
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Crossrefs

Cf. A006254, A124485, A124493, A124494, A124017, A125113, A124514, A124515.
Cf. A071576, A101994, A101320.

Programs

  • Mathematica
    k = 1; Do[If[n < 5, inc = 1, inc = 15];If[Mod[k, inc] > 0, k = k + inc - Mod[k, inc]];While[Nand @@ PrimeQ[Table[2^j, {j, n}]*k - 1], k += inc]; Print[k], {n, 1, 10}] (* Ray Chandler *)

Extensions

Definition corrected and a(10) calculated by Farideh Firoozbakht, Nov 24 2006
a(11)-a(13) from Giovanni Resta, Apr 22 2019

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

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

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

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

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

A101320 Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1, 64*k-1 and 128*k-1 are all primes.

Original entry on oeis.org

15855, 31785, 267300, 280665, 399675, 561330, 946050, 990510, 1022220, 1082115, 1164735, 1283250, 1303875, 1309545, 1514880, 1669065, 1924410, 2850225, 3078675, 3092760, 3492270, 3536385, 3611205, 3920670, 4148970, 4454775
Offset: 1

Views

Author

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

Keywords

Examples

			4*15855-1, 8*15855-1, 16*15855-1, 32*15855-1, 64*15855-1 and 128*15855-1 are primes, so 15855 is a term.

Links

Crossrefs

Cf. A002515.
Subsequence of A005099, A005122, A101790, A101794 and A101994.

Programs

  • Mathematica
    Select[Range[10^6], And @@ PrimeQ[2^Range[2, 7]*# - 1] &] (* Amiram Eldar, May 23 2024 *)
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(4*n-1) && ispseudoprime(8*n-1) && ispseudoprime(16*n-1) && ispseudoprime(32*n-1) && ispseudoprime(64*n-1) && ispseudoprime(128*n-1), print1(n, ", "))) \\ Iain Fox, Nov 23 2017
Showing 1-9 of 9 results.

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

Content is available under The OEIS End-User License Agreement.