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.

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A153045 Numbers k such that 2*k-11 is not a prime.

Original entry on oeis.org

10, 13, 16, 18, 19, 22, 23, 25, 28, 30, 31, 33, 34, 37, 38, 40, 43, 44, 46, 48, 49, 51, 52, 53, 55, 58, 61, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 77, 78, 79, 82, 83, 85, 86, 88, 90, 91, 93, 94, 97, 98, 99, 100, 103, 106, 107, 108, 109, 110, 112, 113, 114
Offset: 1

Views

Author

Vincenzo Librandi, Dec 17 2008

Keywords

Comments

The terms are the values of 2*h*k + k + h + 6, where h and k are positive integers. - Vincenzo Librandi, Jan 19 2013

Links

Crossrefs

Cf. A097338, A153043, A163652, A104275.

Programs

  • Magma
    [n: n in [7..120] | not IsPrime(2*n - 11)]; // Vincenzo Librandi, Oct 11 2012
  • Mathematica
    Select[Range[10,200], !PrimeQ[2*#-11]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)
  • Python
    from sympy import isprime
def ok(n): return n > 6 and not isprime(2*n-11)
print(list(filter(ok, range(115)))) # Michael S. Branicky, Oct 13 2021

Formula

a(n) = 5+A104275(n+1). [R. J. Mathar, Oct 22 2009]

A163655 a(n) = n*(2*n^2 + 5*n + 13)/2.

Original entry on oeis.org

0, 10, 31, 69, 130, 220, 345, 511, 724, 990, 1315, 1705, 2166, 2704, 3325, 4035, 4840, 5746, 6759, 7885, 9130, 10500, 12001, 13639, 15420, 17350, 19435, 21681, 24094, 26680, 29445, 32395, 35536, 38874, 42415, 46165, 50130, 54316, 58729, 63375
Offset: 0

Views

Author

Vincenzo Librandi, Aug 02 2009

Keywords

Links

Crossrefs

Cf. A163652.

Programs

  • Mathematica
    CoefficientList[Series[x*(10-9*x+5*x^2)/(x-1)^4,{x,0,40}],x] (* Vincenzo Librandi, Mar 05 2012 *)
LinearRecurrence[{4,-6,4,-1}, {0,10,31,69}, 50] (* G. C. Greubel, Aug 01 2017 *)
  • PARI
    x='x+O('x^50); concat([0], Vec(x*(10-9*x+5*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 01 2017

Formula

Row sums from A163652: a(n) = Sum_{m=1..n} (2*m*n + m + n + 6).
G.f.: x*(10 - 9*x + 5*x^2)/(x-1)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (1/2)*x*(20 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 01 2017

Extensions

Edited by R. J. Mathar, Aug 05 2009
Showing 1-2 of 2 results.

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