A325209 Numbers k such that Gamma(k - 1/2) has fractional part < 1/2.

3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 24, 25, 26, 31, 32, 33, 36, 37, 39, 41, 42, 46, 48, 49, 51, 53, 56, 61, 62, 63, 66, 69, 70, 71, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 94, 97, 98, 100, 102, 103, 104, 105, 106, 109, 110

Offset

1,1

Comments

Complement of A325210.

Links

Table of n, a(n) for n=1..64.

Example

Approximations for the first 6 values of Gamma(k-1/2) follow:
1.77245, 0.886227, 1.32934, 3.32335, 11.6317, 52.3428.
Exact values are v, v/2, 3v/4, 15v/8, ..., where v = sqrt(Pi) = A002161.

Mathematica

t[n_] := N[Gamma[n - 1/2], 300] ; r = Range[200];
Select[r, FractionalPart[t[#]] < 1/2 &]  (* A325209 *)
Select[r, FractionalPart[t[#]] > 1/2 &]  (* A325210 *)

Crossrefs

Cf. A000142, A002161, A325210.

Sequence in context: A199015 A196098 A099356 * A121543 A080702 A156167

Adjacent sequences: A325206 A325207 A325208 * A325210 A325211 A325212

Keyword

nonn

Author

Clark Kimberling, Apr 09 2019

Status

approved