A183573 a(n) = n + floor(sqrt(2n+1)).

2, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92

Offset: 1

Author

Clark Kimberling, Jan 05 2011

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A047838, A103128, A116940 (complement).

Programs

Maple

seq(n+floor(sqrt(2*n+1)), n=1..100); # Robert Israel, Sep 12 2016

Mathematica

Table[n + Floor@ Sqrt[2 n + 1], {n, 80}] (* Michael De Vlieger, Sep 12 2016 *)

Formula

From Robert Israel, Sep 12 2016: (Start)

a(n+1)=a(n)+2 if n is in A047838, otherwise a(n+1) = a(n)+1.

a(n) = n + A103128(n+1).

G.f.: Theta3(x^2)/(2*(1-x)) + Theta2(x^2)/(2*sqrt(x)*(1-x)) - (1-2*x)*(3-x)/(2*(1-x)^2), where Theta2 and Theta3 are Jacobi Theta functions. (End)