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.

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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

A127590 Numbers n such that 16n+5 is prime.

Original entry on oeis.org

0, 2, 3, 6, 9, 11, 12, 14, 17, 18, 23, 24, 26, 38, 41, 42, 44, 47, 48, 51, 53, 62, 63, 66, 68, 69, 77, 81, 86, 89, 93, 101, 102, 104, 108, 116, 117, 123, 128, 129, 138, 143, 144, 146, 147, 149, 152, 159, 167, 168, 171, 174, 177, 182, 191, 194
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Links

Crossrefs

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[16n + 5], AppendTo[a, n]], {n, 0, 200}]; a
Select[Range[0,200],PrimeQ[16#+5]&] (* Harvey P. Dale, Aug 31 2020 *)
  • PARI
    is(n)=isprime(16*n+5) \\ Charles R Greathouse IV, Feb 17 2017

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

A127591 Numbers k such that 64k+21 is prime.

Original entry on oeis.org

2, 4, 10, 13, 17, 19, 20, 22, 23, 25, 29, 32, 37, 44, 50, 53, 55, 58, 59, 62, 68, 79, 83, 88, 89, 94, 95, 97, 100, 107, 109, 113, 118, 122, 134, 142, 143, 152, 155, 157, 158, 163, 167, 169, 173, 193, 194, 199, 200
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Links

Crossrefs

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127592, A127593, A127594.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[21 + 64 n], AppendTo[a, n]], {n, 0, 200}]; a
Select[Range[200],PrimeQ[64#+21]&] (* Harvey P. Dale, Jan 15 2016 *)

A127592 Primes of the form 64k+21.

Original entry on oeis.org

149, 277, 661, 853, 1109, 1237, 1301, 1429, 1493, 1621, 1877, 2069, 2389, 2837, 3221, 3413, 3541, 3733, 3797, 3989, 4373, 5077, 5333, 5653, 5717, 6037, 6101, 6229, 6421, 6869, 6997, 7253, 7573, 7829, 8597, 9109, 9173, 9749, 9941, 10069, 10133, 10453
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007, Nov 12 2007

Keywords

Comments

All these primes are sums of two squares, also all indices are sums of two squares since we have the identity 64k+21 = 4(4(4k+1)+1)+1.

Links

Crossrefs

Cf. A000040. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127593, A127594.

Programs

  • Magma
    [p: p in PrimesUpTo(11000) | p mod 64 eq 21 ]; // Vincenzo Librandi, Sep 06 2012
  • Mathematica
    a = {}; Do[If[PrimeQ[21 + 64 n], AppendTo[a, 21 + 64 n]], {n, 0, 200}]; a
Select[Prime[Range[1700]], MemberQ[{21}, Mod[#, 64]] &] (* Vincenzo Librandi, Sep 06 2012 *)

A141194 Primes of the form 16k+7.

Original entry on oeis.org

7, 23, 71, 103, 151, 167, 199, 263, 311, 359, 439, 487, 503, 599, 631, 647, 727, 743, 823, 839, 887, 919, 967, 983, 1031, 1063, 1223, 1303, 1319, 1367, 1399, 1447, 1511, 1543, 1559, 1607, 1783, 1831, 1847, 1879, 2039, 2087, 2311, 2423, 2503, 2551, 2647
Offset: 1

Views

Author

T. D. Noe, Jun 12 2008

Keywords

Links

Crossrefs

Cf. A094407, A091968, A127589, A105126, A141195, A141196, A127576.

Programs

A127579 Primes of the form 64n+63.

Original entry on oeis.org

127, 191, 383, 1087, 1151, 1279, 1471, 1663, 2111, 2239, 2687, 2879, 3391, 3583, 3967, 4159, 4799, 5119, 5503, 6079, 6143, 6271, 6719, 6911, 7039, 7103, 7487, 8191, 8447, 8831, 9151, 9343, 9791, 10111, 10303, 10559, 10687, 11071, 11519, 11839
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Links

Crossrefs

Cf. A127575, A127576, A127577, A127578, A127580, A127581.

Programs

  • Magma
    [p: p in PrimesUpTo(12000) | p mod 64 eq 63]; // Vincenzo Librandi, Aug 25 2012
  • Mathematica
    a = {}; Do[If[PrimeQ[64n + 63], AppendTo[a, 64n + 63]], {n, 1, 200}]; a
Select[Prime[Range[4000]], MemberQ[{63}, Mod[#, 64]] &] (* Vincenzo Librandi, Aug 25 2012 *)
Select[Range[63,12000,64],PrimeQ] (* Harvey P. Dale, Mar 01 2015 *)
  • PARI
    forprime(p=2,1e6,if(bitand(p,63)==63,print1(p", "))) \\ Charles R Greathouse IV, May 15 2013

A127593 Primes of the form 256 k + 85.

Original entry on oeis.org

853, 1109, 1621, 1877, 2389, 3413, 5717, 6229, 6997, 7253, 10069, 10837, 11093, 12373, 13397, 16981, 17749, 18517, 18773, 19541, 21589, 22613, 23893, 24917, 27733, 29269, 30293, 31573, 32341, 37717, 39509, 40277, 41813, 43093, 46933
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127594.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[85 + 256 n], AppendTo[a, 85 + 256 n]], {n, 0, 200}]; a
Select[256*Range[200]+85,PrimeQ] (* Harvey P. Dale, Oct 09 2020 *)

A127594 Numbers k such that 256 k + 85 is prime.

Original entry on oeis.org

3, 4, 6, 7, 9, 13, 22, 24, 27, 28, 39, 42, 43, 48, 52, 66, 69, 72, 73, 76, 84, 88, 93, 97, 108, 114, 118, 123, 126, 147, 154, 157, 163, 168, 183, 184, 186, 196, 198
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127593.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[85 + 256 n], AppendTo[a, n]], {n, 0, 200}]; a
Previous Showing 11-20 of 27 results. Next

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