A183298 Complement of A147875.

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Offset: 1

Author

Clark Kimberling, Jan 03 2011

Keywords

• nonn

Crossrefs

Cf. A147875.

Programs

Mathematica

a=5/2; b=3/2;
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[F[n], {n,60}]
Table[G[n], {n,100}]

Python

from math import isqrt
def A183298(n): return n+(m:=isqrt((k:=n<<1)//5))-(k<=m*(5*m+1)) # Chai Wah Wu, Oct 12 2024

Formula

(See the Mathematica code.)

a(n) = n+floor(sqrt(2n/5)) if 2n > floor(sqrt(2n/5))(5*floor(sqrt(2n/5))+1) and a(n) = n+floor(sqrt(2n/5))-1 otherwise. - Chai Wah Wu, Oct 12 2024