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 1-8 of 8 results.

A125220 Numbers k such that binomial(3k, k) - 1 is prime.

Original entry on oeis.org

1, 3, 7, 11, 49, 88, 93, 196, 216, 519, 655, 722, 858, 905, 991, 1654, 2277, 3275, 4214, 5047, 5924, 7359, 7953, 11188, 13286, 14626, 14687, 34365, 36014, 65613, 93663, 101805
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Crossrefs

Cf. A125221 (binomial(3k, k) + 1 is prime).
Cf. A066699 (binomial(2k, k) + 1 is prime).
Cf. A066726 (binomial(2k, k) - 1 is prime).

Programs

  • Mathematica
    Do[f=Binomial[3n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[4300],PrimeQ[Binomial[3#,#]-1]&] (* Harvey P. Dale, Aug 24 2017 *)
  • PARI
    is(n)=binomial(3*n,n)-1 \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(19) from Robert G. Wilson v, Nov 26 2006
a(20)-a(29) from Robert Price, Apr 23 2019
a(30)-a(32) from Georg Grasegger, May 26 2025

A125240 Numbers k such that binomial(4k, k) - 1 is prime.

Original entry on oeis.org

1, 16, 36, 67, 95, 369, 383, 745, 1599, 2006, 2104, 2879, 3061, 9048, 9902, 12369, 15058, 18858, 21287, 22759, 24674, 33899, 43730, 55078, 86085
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Comments

a(26) > 10^5 - Robert Price, Sep 15 2024

Crossrefs

Cf. A125241 = numbers n such that binomial(4n, n) + 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125242, A125243, A125244, A125245.

Programs

  • Mathematica
    Do[f=Binomial[4n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]

Extensions

More terms from Ryan Propper, Mar 28 2007
a(16)-a(23) from Robert Price, Apr 30 2019
a(24)-a(25) from Robert Price, Sep 15 2024

A125241 Numbers k such that binomial(4k, k) + 1 is prime.

Original entry on oeis.org

0, 1, 2, 6, 10, 11, 19, 28, 80, 123, 141, 147, 154, 198, 200, 346, 851, 887, 1038, 1329, 2045, 3228, 3274, 3588, 6794, 8045, 11911, 12184, 12327, 12515, 20089, 38173, 41026, 48914, 71772, 72130, 100726
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Crossrefs

Cf. A125240 = numbers n such that binomial(4n, n) - 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125242, A125243, A125244, A125245.

Programs

  • Mathematica
    Do[f=Binomial[4n, n]+1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[8100],PrimeQ[Binomial[4#,#]+1]&] (* Harvey P. Dale, Aug 24 2014 *)

Extensions

More terms from Ryan Propper, Mar 28 2007
a(1)=0 added by Robert Price, May 01 2019
a(27)-a(34) from Robert Price, May 01 2019
a(35)-a(37) from Georg Grasegger, Jun 02 2025

A125242 Numbers k such that binomial(5k, k) - 1 is prime.

Original entry on oeis.org

5, 71, 111, 187, 239, 247, 473, 628, 847, 1478, 2687, 3530, 5175, 9113, 10968, 15039, 28929, 35649, 43481, 44455, 51269, 63975, 71723
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Comments

a(24) > 10^5. Robert Price, Nov 16 2024

Crossrefs

Cf. A125243 = numbers n such that binomial(5n, n) + 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125240, A125241, A125244, A125245.

Programs

  • Mathematica
    Do[f=Binomial[5n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[45000],PrimeQ[Binomial[5#,#]-1]&] (* Harvey P. Dale, Jan 02 2022 *)

Extensions

More terms from Ryan Propper, Jan 06 2007
a(15)-a(20) from Robert Price, May 03 2019
a(21)-a(23) from Robert Price, Nov 16 2024

A125243 Numbers k such that binomial(5k, k) + 1 is prime.

Original entry on oeis.org

0, 22, 86, 154, 160, 488, 705, 958, 975, 1262, 1932, 2845, 12718, 14434, 20337, 38834, 40433, 44874, 68279, 68724, 89911, 104765
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Comments

a(22) > 100000. - Robert Price, Mar 20 2025

Crossrefs

Cf. A125242, A066699, A066726.
Cf. A125220, A125221, A125240, A125241, A125244, A125245.

Programs

  • Mathematica
    Do[f=Binomial[5n, n]+1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]

Extensions

More terms from Ryan Propper, Jan 05 2007
a(1)=0 prepended and a(13)-a(18) added by Robert Price, May 11 2019
a(19)-a(21) from Robert Price, Mar 20 2025
a(22) from Georg Grasegger, May 06 2025

A125244 Numbers k such that binomial(6k, k) - 1 is prime.

Original entry on oeis.org

1, 7, 17, 22, 43, 343, 381, 461, 543, 923, 1045, 1182, 1486, 1839, 5643, 8260, 9009, 10947, 11793, 15915, 25151, 50923, 57095, 59977, 76513, 83383
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Comments

a(27) > 100000. - Robert Price, May 09 2025

Crossrefs

Cf. A125245 = numbers n such that binomial(6n, n) + 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125240, A125241, A125242, A125243.

Programs

  • Mathematica
    Do[f=Binomial[6n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]

Extensions

More terms from Ryan Propper, Mar 28 2007
a(18)-a(21) from Robert Price, May 13 2019
a(22)-a(23) from Georg Grasegger, May 08 2025
a(24)-a(26) from Robert Price, May 09 2025

A125245 Numbers k such that binomial(6k, k) + 1 is prime.

Original entry on oeis.org

0, 1, 2, 4, 10, 15, 98, 111, 118, 236, 280, 512, 1284, 1303, 1818, 2525, 2692, 4620, 8405, 11539, 13190, 21525, 30338, 48069, 50687, 56208, 56620, 81091, 101488
Offset: 1

Views

Author

Alexander Adamchuk, Nov 25 2006

Keywords

Comments

a(25) > 50000. - Robert Price, May 13 2019

Crossrefs

Cf. A125244 = numbers n such that binomial(6n, n) - 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125240, A125241, A125242, A125243.

Programs

  • Mathematica
    Do[f=Binomial[6n, n]+1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]

Extensions

More terms from Ryan Propper, Mar 28 2007
a(1)=0 and a(20)-a(24) from Robert Price, May 13 2019
a(25)-a(29) from Georg Grasegger, Jun 23 2025

A154119 Numbers k such that binomial(3k,k) is odd and not divisible by 5.

Original entry on oeis.org

0, 1, 5, 8, 16, 33, 40, 41, 65, 66, 80, 81, 128, 130, 133, 138, 165, 325, 328, 330, 640, 641, 650, 656, 658, 1025, 1026, 1028, 1033, 1040, 1041, 2065, 2066, 2080, 2081, 4128, 4130, 4133, 4138, 4165, 4688, 4690, 4753, 4756, 4776, 4778, 5125, 5128, 5130, 5138
Offset: 0

Views

Author

Zak Seidov, Jan 05 2009

Keywords

Comments

From the first 10001 terms of A005809 only 80 are odd and not divisible by 5.

Links

Crossrefs

Cf. A125221 Numbers n such that binomial(3n,n)+1 is prime, A005809 Binomial coefficients C(3n,n).

Programs

  • Mathematica
    (*M6*)Reap[Do[b=Binomial[3n,n];If[OddQ[b]&&Mod[b,10]=/=5,Sow[n]],{n,100}]][[2,1]]
bQ[n_]:=Module[{bi=Binomial[3n,n]},OddQ[bi]&&!Divisible[bi,5]]; Select[Range[0,5300],bQ] (* Harvey P. Dale, Jul 19 2011 *)

Formula

A005809(a(n)) is odd and not divisible by 5.

Extensions

Corrected definition - Harvey P. Dale, Jul 19 2011
Showing 1-8 of 8 results.

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