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 1-2 of 2 results.

A126990 Largest prime preceding geometric mean of prime(n) and prime(n+2).

Original entry on oeis.org

3, 3, 7, 7, 13, 13, 19, 23, 23, 31, 31, 37, 43, 47, 47, 53, 61, 61, 67, 73, 73, 83, 89, 89, 97, 103, 103, 109, 113, 113, 131, 131, 139, 139, 151, 151, 157, 167, 167, 173, 181, 181, 193, 193, 199, 199, 211, 223, 229, 233, 233, 241, 241, 251, 257, 263, 271, 271, 277
Offset: 1

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Author

Artur Jasinski, Jan 01 2007

Keywords

Comments

With duplicates removed, seems to be a subsequence of A105399 and A105792. - M. F. Hasler, Jun 14 2007

References

  • P. Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004.

Links

Crossrefs

Cf. A007917, A073273.

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions` a = {}; Do[AppendTo[a,PreviousPrime[Sqrt[(Prime[x])*(Prime[x + 2])]]], {x, 1, 100}]; a
  • PARI
    A126990(n)={ n=sqrtint(prime(n)*prime(n+2)); if( 0==n%2, n--); while(!isprime(n), n-=2); n } /* then vector(50,n,A126990(n)) displays a list of values, M. F. Hasler, Jun 14 2007 */
  • PARI
    a(n)= precprime(sqrtint(prime(n)*prime(n+2))); \\ Michel Marcus, Nov 07 2013

Formula

a(n) = A007917(A073273(n)). - Michel Marcus, Nov 07 2013

Extensions

Edited by M. F. Hasler, Jun 14 2007
Definition changed so that offset is now 1 by Michel Marcus, Nov 07 2013

A104522 Expansion of (-1+x+3*x^2-x^3)/((x+1)(3*x-1)(x-1)^2).

Original entry on oeis.org

1, 3, 7, 19, 53, 155, 459, 1371, 4105, 12307, 36911, 110723, 332157, 996459, 2989363, 8968075, 26904209, 80712611, 242137815, 726413427, 2179240261, 6537720763, 19613162267, 58839486779, 176518460313, 529555380915, 1588666142719, 4765998428131
Offset: 0

Views

Author

Creighton Dement, Apr 20 2005

Keywords

Comments

A floretion-generated sequence relating to A081250 (Numbers n such that A081249(m)/m^2 has a local minimum for m = n).
Binomial transform starts: 1, 4, 14, 50, 184, 696, 2688, 10528, 41600, 165248, ... - Wesley Ivan Hurt, Sep 12 2014
Floretion Algebra Multiplication Program, FAMP Code: 1famforrokseq[ - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki']

Links

Crossrefs

Cf. A081250, A105792.

Programs

  • Magma
    [(5*3^n+4*(n+1)-(-1)^n)/8 : n in [0..30]]; // Wesley Ivan Hurt, Sep 12 2014
  • Maple
    A104522:=n->(5*3^n+4*(n+1)-(-1)^n)/8: seq(A104522(n), n=0..30); # Wesley Ivan Hurt, Sep 12 2014
  • Mathematica
    CoefficientList[Series[(-1 + x + 3 x^2 - x^3)/((x + 1) (3*x - 1) (x - 1)^2), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 12 2014 *)

Formula

a(n) = (1/8) * (5*3^n + 4*(n+1) - (-1)^n). - Ralf Stephan, Nov 13 2010.
a(n+2) - 2a(n+1) + a(n) = A081250(n+1) - A081250(n).
a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3)+3*a(n-4). - Wesley Ivan Hurt, Sep 12 2014
Showing 1-2 of 2 results.

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

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