A184675 a(n) = n + floor(sqrt(n) + sqrt(n+1)); complement of A184674.

3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83

Offset: 1

Author

Clark Kimberling, Jan 19 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A183867, A184674.

Programs

Maple

A184675:=n->n + floor(sqrt(4*n + 1)); seq(A184675(n), n=1..50); # Wesley Ivan Hurt, Mar 01 2014

Mathematica

a[n_]:=n+Floor[(n/2-1/(2n))^2];
b[n_]:=n+Floor[n^(1/2)+(n+1)^(1/2)];
Table[a[n],{n,1,120}]   (* A184674 *)
Table[b[n],{n,1,120}]   (* A184675 *)

Formula

a(n) = n + floor(sqrt(n) + sqrt(n+1)).

a(n) = n + floor(sqrt(4*n + 1)). [Mircea Merca, Feb 05 2012]