A325209 - OEIS

%I #16 Apr 21 2021 03:55:47

%S 3,4,6,8,9,10,11,12,13,14,15,17,18,19,20,21,24,25,26,31,32,33,36,37,

%T 39,41,42,46,48,49,51,53,56,61,62,63,66,69,70,71,74,75,76,77,79,80,81,

%U 83,84,85,86,87,89,94,97,98,100,102,103,104,105,106,109,110

%N Numbers k such that Gamma(k - 1/2) has fractional part < 1/2.

%C Complement of A325210.

%e Approximations for the first 6 values of Gamma(k-1/2) follow:

%e 1.77245, 0.886227, 1.32934, 3.32335, 11.6317, 52.3428.

%e Exact values are v, v/2, 3v/4, 15v/8, ..., where v = sqrt(Pi) = A002161.

%t t[n_] := N[Gamma[n - 1/2], 300] ; r = Range[200];

%t Select[r, FractionalPart[t[#]] < 1/2 &]  (* A325209 *)

%t Select[r, FractionalPart[t[#]] > 1/2 &]  (* A325210 *)

%Y Cf. A000142, A002161, A325210.

%K nonn

%O 1,1

%A _Clark Kimberling_, Apr 09 2019