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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A073076 Numbers k such that 2*k+1 divides C(2*k,k).

Original entry on oeis.org

97, 136, 178, 192, 199, 292, 313, 332, 448, 467, 472, 478, 487, 535, 542, 577, 604, 617, 697, 773, 790, 797, 852, 885, 940, 962, 967, 997, 1017, 1045, 1096, 1127, 1147, 1165, 1182, 1202, 1237, 1291, 1292, 1319, 1332, 1339, 1345, 1354, 1368, 1397, 1414
Offset: 1

Views

Author

Benoit Cloitre, Aug 17 2002

Keywords

Comments

Integers k such that A056617(k) = 1. - Michel Marcus, May 27 2019
Numbers n such that A005408(n) divides A000984(n). - Felix Fröhlich, May 27 2019

Links

Crossrefs

Cf. A000984, A005408, A056616, A056617, A080394.

Programs

  • Mathematica
    Select[Range@ 1500, Mod[Binomial[2 #, #], 2 # + 1] == 0 &] (* Michael De Vlieger, May 27 2019 *)
  • PARI
    isok(n) = ! (binomial(2*n, n) % (2*n+1)); \\ Michel Marcus, Nov 28 2013

A080395 Even numbers k such that the central binomial coefficient A000984(k, k/2) is divisible by k^2.

Original entry on oeis.org

1848, 2574, 4004, 4290, 6732, 7480, 8398, 12012, 12236, 17710, 20930, 22770, 24570, 24650, 24882, 25080, 25194, 26796, 27132, 30160, 31668, 36540, 36708, 37674, 37944, 38454, 47124, 47740, 51282, 51480, 53200, 57288, 62160, 68376, 69930, 70840, 73260, 75480, 83640
Offset: 1

Views

Author

Labos Elemer, Mar 18 2003

Keywords

Comments

a(n)/2 is a term of A121943 for all n. - Amiram Eldar, Mar 07 2022

Links

Crossrefs

Cf. A001405, A000984, A067348, A080394, A121943.

Programs

  • Mathematica
    Do[s=Binomial[n, n/2]/n^2; If[IntegerQ[s], Print[n]], {n, 1, 50000}]
Select[2Range[50000],Mod[Binomial[#,#/2],#^2]==0&] (* Harvey P. Dale, Jan 27 2025 *)

Extensions

Name corrected and more terms added by Amiram Eldar, Mar 07 2022
Showing 1-2 of 2 results.

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