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 1-8 of 8 results.

A115104 Numbers n such that 4*n^3 + 1 is prime.

Original entry on oeis.org

1, 3, 4, 7, 9, 10, 19, 25, 34, 37, 39, 42, 49, 54, 55, 72, 73, 78, 85, 87, 93, 94, 102, 108, 109, 118, 138, 142, 147, 157, 160, 165, 168, 175, 192, 195, 202, 210, 214, 220, 228, 232, 243, 247, 249, 250, 252, 253, 258, 267, 273, 274, 279, 289, 297
Offset: 1

Views

Author

Parthasarathy Nambi, Mar 02 2006

Keywords

Comments

For any n in this sequence, 3*(4*n^3 + 1) has the same nonzero digits as its prime factors in base 2n. - Ely Golden, Dec 12 2016

Examples

			If n=94 then (4*n^3 + 1) = 3322337 (prime).

Links

Crossrefs

Cf. A001912. See A199307 for the actual primes.
See also A199364, A199365, A199366, A199367, A199368, A199369.

Programs

Extensions

More terms from Stefan Steinerberger, Mar 04 2006

A199367 Primes of the form 4*k^3 - 1.

Original entry on oeis.org

3, 31, 107, 499, 863, 5323, 6911, 13499, 23327, 107999, 131071, 364499, 442367, 530603, 1000187, 1149983, 2634011, 2915999, 3764767, 4121203, 5771587, 6243583, 7263391, 7812499, 9199871, 13499999, 14326307, 14895499, 15185663, 16693123, 19651999, 20000843, 20710867, 24513947, 29659499, 31049567, 33461707, 38654387, 50597347, 53248211, 57395627, 59547743
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199366.

Programs

  • Magma
    [a: n in [1..250] | IsPrime(a) where a is 4*n^3-1]; // Vincenzo Librandi, Nov 23 2011
  • Mathematica
    Select[Table[4n^3-1,{n,1,8000}],PrimeQ] (* Vincenzo Librandi, Nov 23 2011 *)

A199364 Numbers k such that 4k^3 + 3 is prime.

Original entry on oeis.org

0, 1, 5, 10, 14, 20, 28, 34, 38, 49, 55, 59, 61, 80, 98, 103, 118, 133, 145, 146, 154, 160, 185, 196, 206, 224, 229, 241, 245, 250, 251, 320, 325, 334, 376, 383, 385, 388, 398, 416, 418, 440, 451, 454, 475, 476, 481, 488, 490, 493, 496, 500
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199365.

Programs

Extensions

First term added by Vincenzo Librandi, Nov 08 2011

A199365 Primes of the form 4n^3 + 3.

Original entry on oeis.org

3, 7, 503, 4003, 10979, 32003, 87811, 157219, 219491, 470599, 665503, 821519, 907927, 2048003, 3764771, 4370911, 6572131, 9410551, 12194503, 12448547, 14609059, 16384003, 25326503, 30118147, 34967267, 44957699, 48035959, 55990087, 58824503, 62500003, 63253007, 131072003
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199364.

Programs

  • Magma
    [a: n in [0..300] | IsPrime(a) where a is 4*n^3+3]; // Vincenzo Librandi, Nov 27 2011
  • Mathematica
    Select[Table[4n^3+3,{n,0,6000}],PrimeQ] (* Vincenzo Librandi, Nov 27 2011 *)

Formula

a(n) = 4*A199364(n)^3 + 3.

Extensions

First term inserted by Vincenzo Librandi, Nov 27 2011

A199366 Numbers k such that 4*k^3-1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 11, 12, 15, 18, 30, 32, 45, 48, 51, 63, 66, 87, 90, 98, 101, 113, 116, 122, 125, 132, 150, 153, 155, 156, 161, 170, 171, 173, 183, 195, 198, 203, 213, 233, 237, 243, 246, 260, 266, 282, 288, 291, 297, 300, 302, 305, 308, 321, 335, 341, 342, 347, 366, 371, 377, 381, 386, 393, 398, 401, 402, 407, 408, 411, 423, 425, 426, 437, 443, 452, 455, 456
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199367.

Programs

A199368 Numbers k such that 4k^3 - 3 is prime.

Original entry on oeis.org

2, 14, 16, 22, 25, 29, 49, 64, 74, 77, 86, 91, 112, 121, 127, 134, 137, 140, 151, 161, 179, 197, 214, 221, 226, 254, 259, 284, 287, 296, 302, 305, 310, 347, 361, 364, 365, 380, 382, 392, 394, 401, 406, 407, 415, 469, 497
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199369.

Programs

A199369 Primes of the form 4*n^3 - 3.

Original entry on oeis.org

29, 10973, 16381, 42589, 62497, 97553, 470593, 1048573, 1620893, 1826129, 2544221, 3014281, 5619709, 7086241, 8193529, 9624413, 10285409, 10975997, 13771801, 16693121, 22941353, 30581489, 39201373, 43175441, 46172701, 65548253, 69495913, 91625213, 94559609, 103737341, 110174429, 113490497, 119163997, 167127689, 188183521, 192914173, 194508497
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2011

Keywords

Comments

See comment in A199307.

Links

Crossrefs

Cf. A199307, A199368.

Programs

  • Magma
    [a: n in [1..250] | IsPrime(a) where a is 4*n^3-3]; // Vincenzo Librandi, Nov 23 2011
  • Mathematica
    Select[Table[4n^3-3,{n,1,5000}],PrimeQ]

A207837 Primes of the form 5*k^4 + 1.

Original entry on oeis.org

6481, 103681, 844480081, 1036800001, 55099802881, 63727534081, 115672050001, 155584800001, 307529920081, 322620641281, 425152800001, 1019640545281, 1633266996481, 1739461754881, 2489356800001, 2634683086081, 2944329626881, 5285935072081, 6360160441681
Offset: 1

Views

Author

Bruno Berselli, Feb 21 2012

Keywords

Comments

Also primes of the form 6480*k^4+1.

Links

Crossrefs

Cf. A207838 (values of k).
Subsequence of A137530.
Primes of the form k*n^(k-1)+1: A065091, A002648, A199307.

Programs

  • Magma
    [6480*n^4+1: n in [1..181] | IsPrime(6480*n^4+1)];
  • Mathematica
    Select[5 Range[1086]^4 + 1, PrimeQ] (* by definition *)
  • PARI
    for(n=1, 181, r=6480*n^4+1; if(isprime(r), print1(r", ")));

Formula

a(n) = 5*A207838(n)^4 + 1. - Paul F. Marrero Romero, Dec 07 2023
Showing 1-8 of 8 results.

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

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