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Positions of zeros in A065345.
6

%I #19 Dec 12 2024 14:53:26

%S 8,11,16,18,19,20,23,26,35,38,41,42,43,44,46,48,49,50,51,53,54,55,56,

%T 58,59,60,64,66,67,68,70,71,72,73,74,75,76,80,83,86,89,92,95,96,97,98,

%U 99,100,101,102,103,104,107,110,113,116,119,123,124,128,130,131,134

%N Positions of zeros in A065345.

%H Harry J. Smith, <a href="/A065348/b065348.txt">Table of n, a(n) for n = 1..1000</a>

%H Carl Pomerance, <a href="https://math.dartmouth.edu/~carlp/catalan5.pdf">Divisors of the middle binomial coefficient</a>, Amer. Math. Monthly, 112 (2015), 636-644.

%t ris = {}; Do[If[Mod[Binomial[2 n, n], (n + 1) (n + 2) (n + 3)] == 0,

%t AppendTo[ris, n]], {n, 150}]; ris (* _Bruno Berselli_, Jan 06 2014 *)

%o (PARI) isok(k) = { binomial(2*k, k) % ((k + 1)*(k + 2)*(k + 3)) == 0 } \\ _Harry J. Smith_, Oct 17 2009

%Y Cf. A000108, A065344, A065345, A065346, A065347, A065349.

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 30 2001