A183301 Complement of A014105.

1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

Author

Clark Kimberling, Jan 03 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A014105, A339183.

Programs

Mathematica

a=2; b=1;
F[n_]:=a*n^2+b*n;
R[n_]:=(n/a+((b-1)/(2a))^2)^(1/2);
G[n_]:=n-1+Ceiling[R[n]-(b-1)/(2a)];
Table[G[n], {n,100}]

Python

from math import isqrt
def A183301(n): return n+isqrt(n-1>>1) # Chai Wah Wu, Nov 04 2024

Formula

a(n) = n + floor(sqrt((n-1)/2)) = n + A339183(n-1). - Aaron J Grech, Jul 30 2024