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A125220

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

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

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 *)

PROG

(PARI) is(n)=binomial(3*n, n)-1 \\ Charles R Greathouse IV, Feb 17 2017

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).

Sequence in context: A358311 A217383 A005372 * A016081 A287301 A105762

Adjacent sequences: A125217 A125218 A125219 * A125221 A125222 A125223

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Nov 25 2006

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

STATUS

approved

URL: https://oeis.org/A125220

⇱ A125220 - OEIS