A183294 Complement of A005449.

1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 1

Author

Clark Kimberling, Jan 03 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A005449, A180447.

Programs

Mathematica

a=3/2; b=1/2;
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}]

PARI

a(n) = n + (sqrtint(24*n)+1)\6; \\ Kevin Ryde, Sep 01 2024

Python

from math import isqrt
def A183294(n): return n+(m:=isqrt((k:=n<<1)//3))+(k>=m*(3*m+5)+4) # Chai Wah Wu, Nov 04 2024

Formula

(See the Mathematica code.)

a(n) = n + A180447(n-1). - Kevin Ryde, Sep 01 2024

a(n) = n+m+1 if 2n>=m(3m+5)+4 and a(n) = n+m otherwise where m = floor(sqrt(2n/3)). - Chai Wah Wu, Nov 04 2024