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 1-4 of 4 results.

A066436 Primes of the form 2*n^2 - 1.

Original entry on oeis.org

7, 17, 31, 71, 97, 127, 199, 241, 337, 449, 577, 647, 881, 967, 1151, 1249, 1567, 2311, 2591, 2887, 3041, 3361, 3527, 3697, 4049, 4231, 4801, 4999, 5407, 6271, 6961, 7687, 7937, 8191, 9521, 10657, 11551, 12799, 13121, 14449, 15137, 16561
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2002

Keywords

Comments

It is conjectured that this sequence is infinite.
Also primes p such that 8p + 8 is a square. - Cino Hilliard, Dec 18 2003
Also primes p such that 2p+2 is square; also primes p such that (p+1)/2 is square. - Ray Chandler, Sep 15 2005
Arithmetic numbers which are squares, A003601(p)=A000290(k), p prime, k integer. sigma_1(p)/sigma_0(p)=k^2; p prime, k integer. - Ctibor O. Zizka, Jul 14 2008

References

  • D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

Links

Crossrefs

See A066049 for the values of n, see A091176 for prime index.
Cf. A090697, A110558, A003601, A000290.

Programs

  • Magma
    [ p: n in [1..100] | IsPrime(p) where p is 2*n^2-1 ]; // Klaus Brockhaus, Dec 29 2008
  • Mathematica
    Select[2*Range[200]^2-1,PrimeQ] (* Harvey P. Dale, Aug 29 2016 *)
  • PARI
    { n=0; for (m=1, 10^9, p=2*m^2 - 1; if (isprime(p), write("b066436.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 14 2010

A066049 Numbers n such that 2*n^2 - 1 is a prime.

Original entry on oeis.org

2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 18, 21, 22, 24, 25, 28, 34, 36, 38, 39, 41, 42, 43, 45, 46, 49, 50, 52, 56, 59, 62, 63, 64, 69, 73, 76, 80, 81, 85, 87, 91, 92, 95, 98, 102, 108, 109, 112, 113, 115, 118, 125, 126, 127, 132, 134, 137, 140, 141, 143, 153, 154, 155
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2002

Keywords

Comments

It is conjectured that this sequence is infinite.
A066436 gives resulting primes p such that (p+1)/2 is square. - Ray Chandler

References

  • D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

Links

Crossrefs

Cf. A028870, A066436, A090697, A091176, A110558.

Programs

  • Mathematica
    Select[Range[200],PrimeQ[2#^2-1]&] (* Harvey P. Dale, Jun 14 2011 *)
  • PARI
    { n=0; for (m=1, 10^9, if (isprime(2*m^2 - 1), write("b066049.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 08 2009

Formula

a(n) = A090697(n)/2 = A110558(n)/4. - Ray Chandler, Sep 15 2005
a(n) = A160697(n+1). - Reinhard Zumkeller, May 24 2009

Extensions

Extended by Ray Chandler, Sep 15 2005

A091176 Numbers n such that prime(n) is of the form 2*k^2 - 1.

Original entry on oeis.org

4, 7, 11, 20, 25, 31, 46, 53, 68, 87, 106, 118, 152, 163, 190, 204, 247, 344, 377, 418, 436, 474, 492, 516, 558, 580, 647, 669, 713, 816, 894, 975, 1003, 1028, 1179, 1300, 1392, 1526, 1561, 1695, 1768, 1917, 1952, 2069, 2177, 2343, 2601, 2643, 2769, 2812
Offset: 1

Views

Author

Ray Chandler, Dec 25 2003

Keywords

Comments

A066436 indexed by A000040.

Links

Crossrefs

Cf. A066049, A066436, A090697, A110558.

Programs

Formula

A000040(n) = A066436(n).

A090697 Numbers n such that n^2/2 - 1 is a prime.

Original entry on oeis.org

4, 6, 8, 12, 14, 16, 20, 22, 26, 30, 34, 36, 42, 44, 48, 50, 56, 68, 72, 76, 78, 82, 84, 86, 90, 92, 98, 100, 104, 112, 118, 124, 126, 128, 138, 146, 152, 160, 162, 170, 174, 182, 184, 190, 196, 204, 216, 218, 224, 226, 230, 236, 250, 252, 254, 264, 268, 274, 280
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 20 2003

Keywords

Comments

A066436 gives resulting primes p such that 2p+2 is square. - Ray Chandler, Dec 25 2003

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Links

Crossrefs

Cf. A066049, A066436, A091176, A110558.

Programs

  • Mathematica
    Select[Range[2,300,2],PrimeQ[#^2/2-1]&] (* Harvey P. Dale, Apr 05 2014 *)
  • PARI
    isok(n) = !(n % 2) && isprime(n^2/2 - 1); \\ Michel Marcus, Jul 23 2016

Formula

a(n) = 2*A066049(n) = A110558(n)/2. - Ray Chandler, Dec 25 2003

Extensions

Corrected and extended by Ray Chandler, Dec 25 2003
Showing 1-4 of 4 results.

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

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