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Positions of zeros in A065346.
9

%I #17 Dec 12 2024 14:54:18

%S 19,41,42,43,49,50,53,54,55,58,67,71,74,75,95,97,98,99,102,103,123,

%T 135,138,139,145,149,153,154,155,159,163,165,166,167,168,169,170,173,

%U 174,175,178,179,180,183,184,185,191,193,194,195,197,198,199,200,201,202

%N Positions of zeros in A065346.

%H Harry J. Smith, <a href="/A065349/b065349.txt">Table of n, a(n) for n = 1..1000</a>

%H C. 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) (n + 4)] == 0, AppendTo[ris, n]], {n, 250}]; ris (* _Bruno Berselli_, Jan 06 2014 *)

%o (PARI) isok(k) = { binomial(2*k, k) % ((k + 1)*(k + 2)*(k + 3)*(k + 4)) == 0 } \\ _Harry J. Smith_, Oct 17 2009

%Y Cf. A000108, A065344, A065345, A065346, A065347, A065348.

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 30 2001