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.

A138837 Non-Mersenne primes: A000040 \ A000668.

Original entry on oeis.org

2, 5, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283
Offset: 1

Views

Author

Omar E. Pol, Apr 03 2008

Keywords

Comments

Primes that are not Mersenne primes A000668.
Pandigital primes in base 2. (Pandigital interpreted as including all digits, not necessarily only once each.) - Franklin T. Adams-Watters, May 11 2011
Primes whose sum of divisors is not a power of 2. - Omar E. Pol, Dec 19 2016

Crossrefs

Programs

  • Mathematica
    max = 300; Complement[Prime[Range[PrimePi[max]]], 2^Range[Ceiling[Log[2, max]]] - 1] (* Alonso del Arte, Dec 30 2013 *)
  • PARI
    is_A138837(n)={isprime(n)&&1<M. F. Hasler, Feb 05 2014

Formula

A138837 = A000040 \ A000668. - M. F. Hasler, Feb 09 2014

Extensions

New name from Omar E. Pol, Jan 02 2014

A163815 a(n) = n*(2*n^2 + 5*n + 3).

Original entry on oeis.org

0, 10, 42, 108, 220, 390, 630, 952, 1368, 1890, 2530, 3300, 4212, 5278, 6510, 7920, 9520, 11322, 13338, 15580, 18060, 20790, 23782, 27048, 30600, 34450, 38610, 43092, 47908, 53070, 58590, 64480, 70752, 77418, 84490, 91980, 99900, 108262, 117078, 126360, 136120
Offset: 0

Views

Author

Vincenzo Librandi, Aug 04 2009

Keywords

Crossrefs

Programs

  • Mathematica
    CoefficientList[Series[2*x*(5+x)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 10, 42, 108}, 50](* Vincenzo Librandi, Mar 06 2012 *)
  • PARI
    x='x+O('x^50); concat([0], Vec(2*x*(5+x)/(x-1)^4)) \\ G. C. Greubel, Aug 04 2017

Formula

Row sums from A155151: a(n) = Sum_{m=1..n} 2*(2*m*n + m + n + 1).
a(n) = 2*A160378(n+1).
G.f.: 2*x*(5+x)/(x-1)^4.
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
E.g.f.: (2*x^3 + 11*x^2 + 10*x)*exp(x). - G. C. Greubel, Aug 04 2017

Extensions

Edited and a(4) corrected by R. J. Mathar, Aug 05 2009

A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

Original entry on oeis.org

7, 13, 23, 19, 33, 47, 25, 43, 61, 79, 31, 53, 75, 97, 119, 37, 63, 89, 115, 141, 167, 43, 73, 103, 133, 163, 193, 223, 49, 83, 117, 151, 185, 219, 253, 287, 55, 93, 131, 169, 207, 245, 283, 321, 359, 61, 103, 145, 187, 229, 271, 313, 355, 397, 439, 67, 113, 159
Offset: 1

Views

Author

Vincenzo Librandi, Aug 03 2009

Keywords

Comments

2 + T(n,m) = (2*n+1)*(2*m+1) are composite numbers. - clarified by R. J. Mathar, Oct 16 2009
First column: A016921, second column: A017305, third column: A126980. - Vincenzo Librandi, Nov 21 2012

Examples

			Triangle begins:
   7;
  13,  23;
  19,  33,  47;
  25,  43,  61,  79;
  31,  53,  75,  97, 119;
  37,  63,  89, 115, 141, 167;
  43,  73, 103, 133, 163, 193, 223;
  49,  83, 117, 151, 185, 219, 253, 287;
  55,  93, 131, 169, 207, 245, 283, 321, 359;
  61, 103, 145, 187, 229, 271, 313, 355, 397, 439;
		

Crossrefs

Programs

  • Magma
    [4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
    
  • Mathematica
    t[n_,k_]:=4 n*k + 2n + 2k - 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)
  • PARI
    for(n=1,10, for(k=1,n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ G. C. Greubel, Aug 02 2017

Formula

T(n,m) = A155151(n,m) - 3 = A155156(n,m) - 1. - R. J. Mathar, Oct 16 2009
Showing 1-3 of 3 results.