A385683 Complement of A030511.

1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Author

Chai Wah Wu, Aug 04 2025

Keywords

• nonn
• easy

Comments

Positive numbers not of the form floor(2*k^2/3).

Crossrefs

Cf. A030511.

Programs

Mathematica

m[n_]:=Floor[Sqrt[3(n-1)/2]];a[n_]:=If[n+m[n]>Floor[2(m[n]+1)^2/3],n+m[n],n+m[n]-1];Array[a,67] (* James C. McMahon, Aug 06 2025 *)

Python

from math import isqrt
def A385683(n): return n+(m:=isqrt(3*(n-1)>>1))-(n+m<=((m+1)**2<<1)//3)

Formula

a(n) = n+m if n+m>floor(2*(m+1)^2/3) and a(n) = n+m-1 otherwise where m = floor(sqrt(3*(n-1)/2)).