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.

A154617 Eleven times hexagonal numbers: a(n) = 11*n*(2*n-1).

Original entry on oeis.org

0, 11, 66, 165, 308, 495, 726, 1001, 1320, 1683, 2090, 2541, 3036, 3575, 4158, 4785, 5456, 6171, 6930, 7733, 8580, 9471, 10406, 11385, 12408, 13475, 14586, 15741, 16940, 18183, 19470, 20801, 22176, 23595, 25058, 26565, 28116, 29711, 31350, 33033, 34760, 36531, 38346
Offset: 0

Views

Author

Omar E. Pol, Jan 13 2009

Keywords

Comments

Sequence found by reading the line from 0, in the direction 0, 11, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. - Omar E. Pol, Sep 18 2011

Links

Crossrefs

Cf. A000384, A002939, A094159, A152745, A153781, A195313.

Programs

Formula

a(n) = 22*n^2 - 11*n = 11*A000384(n).
a(n) = a(n-1) + 44*n - 33 (with a(0)=0). - Vincenzo Librandi, Dec 15 2010
From Elmo R. Oliveira, Dec 15 2024: (Start)
G.f.: 11*x*(1 + 3*x)/(1 - x)^3.
E.g.f.: 11*x*(1 + 2*x)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)

A144561 Prime p such that p^2+13p+23 is prime.

Original entry on oeis.org

2, 3, 5, 7, 19, 37, 41, 47, 59, 71, 73, 103, 157, 163, 211, 227, 229, 239, 283, 293, 311, 313, 337, 353, 359, 367, 419, 443, 463, 499, 521, 523, 577, 619, 643, 647, 653, 661, 733, 751, 787, 839, 853, 863, 877, 883, 929, 1021, 1069, 1087, 1123, 1129, 1163
Offset: 1

Views

Author

Vincenzo Librandi, Jan 03 2009

Keywords

Links

Crossrefs

Cf. A153781.

Programs

  • Magma
    [p: p in PrimesUpTo(1500) | IsPrime(p^2+13*p+23)] // Vincenzo Librandi, Aug 30 2012
  • Maple
    a := proc (n) if isprime(n) = true and isprime(n^2+13*n+23) = true then n else end if end proc: seq(a(n), n = 2 .. 1300); # Emeric Deutsch, Jan 20 2009
  • Mathematica
    Select[Prime[Range[200]], PrimeQ[#^2 + 13 # + 23] &] (* Vincenzo Librandi, Aug 30 2012 *)
  • PARI
    isok(p) = isprime(p) && isprime(p^2+13*p+23); \\ Michel Marcus, Feb 10 2018

Extensions

Extended by Emeric Deutsch, Jan 20 2009
Showing 1-2 of 2 results.

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