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.

A201781 Primes of the form 3*m^2 - 8.

Original entry on oeis.org

19, 67, 139, 499, 859, 1579, 1867, 2179, 3259, 4099, 6067, 6619, 8419, 9067, 9739, 22699, 25939, 27067, 28219, 38299, 39667, 46867, 54667, 56299, 61339, 63067, 73939, 79699, 81667, 89779, 91867, 93979, 100459, 102667, 114067, 123619
Offset: 1

Views

Author

Vincenzo Librandi, Dec 05 2011

Keywords

Comments

m is a member of A063241. - Bruno Berselli, Feb 16 2016

Links

Crossrefs

Cf. A089682, A201715, A201716, A201717, A201718.

Programs

  • Magma
    [a: n in [2..300] | IsPrime(a) where a is 3*n^2-8];
  • Mathematica
    Select[Table[3n^2 - 8, {n, 2, 1000}], PrimeQ]

A063213 Dimension of the space of weight 2n cuspidal newforms for Gamma_0(45).

Original entry on oeis.org

1, 5, 9, 11, 15, 19, 21, 25, 29, 31, 35, 39, 41, 45, 49, 51, 55, 59, 61, 65, 69, 71, 75, 79, 81, 85, 89, 91, 95, 99, 101, 105, 109, 111, 115, 119, 121, 125, 129, 131, 135, 139, 141, 145, 149, 151, 155, 159, 161, 165
Offset: 1

Views

Author

N. J. A. Sloane, Jul 10 2001

Keywords

Comments

The sequence lists the odd numbers ending with 1, 5 and 9. This follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016

Links

Crossrefs

Cf. A063241.

Formula

G.f.: x - x^2*(-5-4*x-2*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 15 2015
a(n) = 4*n - 2*floor(n/3 - 1/3) - 3. This formula follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016

A215205 a(n) = (-1)^n * (A060819(n) + A060819(n+1)).

Original entry on oeis.org

1, -2, 4, -4, 6, -8, 10, -9, 11, -14, 16, -14, 16, -20, 22, -19, 21, -26, 28, -24, 26, -32, 34, -29, 31, -38, 40, -34, 36, -44, 46, -39, 41, -50, 52, -44, 46, -56, 58, -49, 51, -62, 64, -54, 56, -68, 70, -59, 61, -74, 76, -64, 66, -80, 82, -69, 71, -86, 88, -74, 76, -92, 94, -79, 81, -98, 100, -84
Offset: 0

Views

Author

Paul Curtz, Aug 06 2012

Keywords

Comments

a(-1)=1=a(0).
a(n) - a(n-1) = b(n) = 0, -3, 6, -8, 10, -14, 18, -19, 20, -25, 30, -30, 30, -36, 42, -41, ... .
Missing terms in abs(a(n)):
PIII(n) = 0, 3, 5, 7, 12, 13, 15, 17, 18, 23, 25, 27, 30, 33, 35, 37, 42, ... . See A063241(n+1) and 6*A047222(n+1).
Quasipolynomial of order 4. - Charles R Greathouse IV, Aug 06 2012

Links

Crossrefs

Cf. A016861, A016933, A016957, A016897.

Programs

  • Mathematica
    a[n_] := Switch[Mod[n, 4], 0, 5n/4+1, 1, (-3n-1)/2, 2, 3n/2+1, 3, (-5n-1)/4]; Table[a[n], {n, 0, 67}] (* Jean-François Alcover, Nov 08 2012 *)

Formula

a(4*n) = 1+5*n, a(1+4*n) = -2-6*n, a(2+4*n) = 4+6*n, a(3+4*n) = -4-5*n.
a(n+4) - a(n) = period of length 4: repeat 5,-6, 6, -5.
a(n) = 2*a(n-4) + a(n-8).
G.f. ( -1+x-3*x^2-3*x^4+x^3+x^5-x^6 ) / ( (x-1)*(1+x)^2*(x^2+1)^2 ). - R. J. Mathar, Aug 07 2012
a(n) = (5+(2*n+1)*(11*(-1)^n-(-1)^((2*n-1+(-1)^n)/4))+(-1)^((6*n-1 +(-1)^n)/4))/16. - Luce ETIENNE, Jun 05 2015
Showing 1-3 of 3 results.

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

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