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 1-3 of 3 results.

A155737 Primes of the form 4*n^2 + 2*n -1.

Original entry on oeis.org

5, 19, 41, 71, 109, 271, 419, 599, 701, 811, 929, 1481, 1979, 2161, 2351, 2549, 2969, 3191, 3659, 4159, 4421, 4691, 4969, 5851, 7481, 8929, 9311, 10099, 13109, 14519, 16001, 17029, 18089, 19181, 19739, 20879, 22051, 23869, 25121, 25759, 27059
Offset: 1

Views

Author

Vincenzo Librandi, Jan 26 2009

Keywords

Comments

Primes in A125202. - Klaus Purath, Dec 09 2020

Links

Crossrefs

Cf. A155736, A155738, A125202.

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is  4*n^2+2*n-1]; // Vincenzo Librandi, Jul 23 2012
  • Mathematica
    Select[Table[4n^2+2n-1,{n,0,200}],PrimeQ] (* Vincenzo Librandi, Jul 23 2012 *)
  • PARI
    (for (n=0, 100, if (isprime (k=4*n^2+2*n-1), print1 (k, ", ")))); \\ Vincenzo Librandi, Jul 23 2012

Extensions

Incorrect formula deleted by N. J. A. Sloane, Jun 16 2010

A155738 Primes p such that 4*p^2+2*p-1 is also prime.

Original entry on oeis.org

2, 3, 5, 13, 19, 23, 43, 47, 67, 79, 103, 109, 149, 157, 179, 193, 239, 353, 373, 397, 419, 487, 499, 503, 523, 547, 563, 569, 587, 619, 677, 683, 787, 797, 839, 853, 863, 929, 1013, 1093, 1193, 1229, 1289, 1303, 1319, 1423, 1433, 1499, 1553, 1619, 1669, 1733
Offset: 1

Views

Author

Vincenzo Librandi, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155736, A155737.

Programs

  • Magma
    [p: p in PrimesUpTo(1800)| IsPrime(4*p^2 + 2*p - 1)]; // Vincenzo Librandi, Oct 30 2012
  • Mathematica
    Select[Prime[Range[400]],PrimeQ[4#^2+2#-1]&]  (* Harvey P. Dale, Mar 22 2011 *)

Formula

A155736 INTERSECT A000040. [R. J. Mathar, Jan 05 2011]

A241266 Numbers n such that 4*n^2+2*n-1 is not prime.

Original entry on oeis.org

6, 7, 9, 11, 16, 17, 18, 20, 21, 26, 29, 31, 36, 37, 39, 40, 41, 42, 44, 45, 46, 49, 51, 52, 53, 54, 55, 56, 58, 59, 61, 62, 64, 66, 68, 71, 73, 75, 76, 78, 81, 83, 84, 85, 86, 89, 91, 95, 96, 97, 99, 100, 101, 102, 104, 105, 106, 107, 108, 111, 112, 113, 114
Offset: 1

Views

Author

Vincenzo Librandi, Apr 20 2014

Keywords

Examples

			7 is in this sequence because 4*7^2+2*7-1 = 209 = 11*19.

Links

Crossrefs

Complement of A155736.

Programs

  • Magma
    [n: n in [1..150] |not IsPrime(4*n^2+2*n-1)];
  • Mathematica
    Select[Range[200], ! PrimeQ[4 #^2 + 2 # - 1] &]
Showing 1-3 of 3 results.

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

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