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 1-10 of 16 results. Next

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

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

A124065 Numbers k such that 8*k - 1 and 8*k + 1 are twin primes.

Original entry on oeis.org

9, 24, 30, 39, 54, 75, 129, 144, 165, 186, 201, 234, 261, 264, 324, 336, 339, 375, 390, 396, 420, 441, 459, 471, 516, 534, 600, 621, 654, 660, 690, 705, 735, 795, 819, 849, 870, 891, 936, 945, 1011, 1029, 1125, 1155, 1179, 1215, 1221, 1251, 1284, 1395, 1419
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Examples

			9 is in the sequence since 8*9 - 1 = 71 and 8*9 + 1 = 73 are twin primes.

Links

Crossrefs

Intersection of A005122 and A005123.
Cf. A040040, A045753, A002822, A124518, A124519, A124520, A124521, A124522, A063983.

Programs

  • Magma
    [n: n in [1..2000] | IsPrime(8*n+1) and IsPrime(8*n-1)] // Vincenzo Librandi, Mar 08 2010
  • Mathematica
    Select[Range[1500], And @@ PrimeQ[{-1, 1} + 8# ] &] (* Ray Chandler, Nov 16 2006 *)
  • Python
    from sympy import isprime
def ok(n): return isprime(8*n - 1) and isprime(8*n + 1)
print(list(filter(ok, range(1420)))) # Michael S. Branicky, Sep 24 2021

Extensions

Extended by Ray Chandler, Nov 16 2006

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

A153766 Numbers n such that 8n-9 is prime.

Original entry on oeis.org

2, 4, 5, 7, 10, 11, 14, 17, 20, 22, 25, 26, 29, 31, 34, 35, 40, 46, 47, 49, 55, 56, 59, 61, 62, 64, 76, 77, 80, 82, 91, 92, 94, 95, 104, 106, 109, 112, 115, 116, 122, 124, 125, 130, 131, 134, 137, 139, 145, 154, 155, 161, 164, 166, 167, 172, 176, 179, 181, 182, 185, 187
Offset: 1

Views

Author

Vincenzo Librandi, Jan 01 2009

Keywords

Comments

One more than the associated value in A005122. - R. J. Mathar, Jan 05 2011

Links

Crossrefs

Cf. A005122, A153767.

Programs

Extensions

83 replaced by 82 from R. J. Mathar, Jan 07 2009

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

A265502 Numbers n such that n*2^1279 - 1 is prime.

Original entry on oeis.org

1, 139, 433, 1563, 2095, 2254, 2871, 3751, 4003, 4338, 4843, 6015, 6331, 6933, 7324, 7345, 7485, 7719, 7836, 8070, 8413, 9018, 9840, 9898, 9915, 9931, 10611, 11215, 11356, 11418, 11560, 11740, 12010, 12673, 13039, 13056, 13225, 14136, 14271, 14380, 14974, 15084
Offset: 1

Views

Author

Vardan Semerjyan, Dec 09 2015

Keywords

Comments

The exponent of 2 in the expression, 1279, is a Mersenne exponent.

Examples

			n = 1 is a term since 2^1279 - 1 is prime (the 15th Mersenne prime).

Links

Crossrefs

Cf. A000043, A001348, A005122.

Programs

  • MATLAB
    if isprime(n*2^1279-1)
disp(n)
end
  • Magma
    [n: n in [1..10^4] |IsPrime(n*2^1279-1)]; // Vincenzo Librandi, Dec 10 2015
  • Mathematica
    Select[Range@ 11500, PrimeQ[# 2^1279 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)
  • PARI
    is(n)=ispseudoprime(n*2^1279 - 1) \\ Anders Hellström, Dec 09 2015

Extensions

Terms a(31) and beyond from Andrew Howroyd, Dec 23 2019

A123978 Numbers k for which 8*k+1, 8*k+3 and 8*k+7 are primes.

Original entry on oeis.org

2, 5, 80, 107, 110, 185, 260, 332, 500, 1067, 1307, 1472, 1625, 1760, 1790, 1955, 2255, 2612, 2627, 2672, 2882, 2945, 3197, 3335, 3467, 3965, 4007, 4037, 4040, 4202, 4355, 4880, 5147, 5252, 5525, 6242, 6812, 6917, 6977, 7430, 7787, 8192, 8612, 8657, 8720
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2006

Keywords

Links

Crossrefs

Cf. A005122, A005123, A005124.

Programs

  • Mathematica
    Select[Range[10^4], And @@ PrimeQ /@ ({1, 3, 7} + 8#) &] (* Ray Chandler, Nov 05 2006 *)

Extensions

Extended by Ray Chandler, Nov 05 2006

A123980 Numbers k for which 8*k+1, 8*k+5 and 8*k+7 are primes.

Original entry on oeis.org

12, 24, 57, 162, 234, 249, 267, 297, 432, 519, 564, 717, 969, 984, 1167, 1179, 1389, 1734, 2007, 2364, 2427, 2544, 2664, 2769, 2784, 3582, 3627, 3819, 3897, 4089, 4287, 5244, 5307, 5337, 5472, 5577, 5667, 5727, 5967, 6084, 6102, 6399, 6522, 6822, 6987
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2006

Keywords

Links

Crossrefs

Cf. A005122, A005123, A005124, A105133.

Programs

  • Mathematica
    Select[Range[7000], And @@ PrimeQ /@ ({1, 5, 7} + 8#) &] (* Ray Chandler, Nov 05 2006 *)

Extensions

Extended by Ray Chandler, Nov 05 2006

A123983 Numbers k for which 8*k+1, 8*k+5, 8*k+7 and 8*k+11 are primes.

Original entry on oeis.org

12, 57, 162, 249, 432, 564, 984, 1734, 2007, 2427, 2664, 2784, 3627, 5307, 5472, 5727, 6399, 7614, 11082, 11547, 11607, 11694, 14127, 14274, 14484, 14862, 15117, 17049, 19104, 19422, 20577, 25677, 27612, 27714, 28152, 29307, 32232, 34602, 35592
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2006

Keywords

Links

Crossrefs

Cf. A005122, A005123, A005124, A005125, A105133.

Programs

  • Maple
    isA123983 := proc(n) RETURN( isprime(8*n+1) and isprime(8*n+5) and isprime(8*n+7) and isprime(8*n+11) ) ; end: for n from 1 to 7000 do if isA123983(n) then printf("%d,",n) ; fi ; od ; # R. J. Mathar, Nov 06 2006
  • Mathematica
    Select[Range[37000], And @@ PrimeQ /@ ({1, 5, 7, 11} + 8#) &] (* Ray Chandler, Nov 05 2006 *)

Extensions

Edited and extended by Ray Chandler and R. J. Mathar, Nov 05 2006
Showing 1-10 of 16 results. Next

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