A183292 Complement of A055999.

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90

Offset

1,2

Links

Table of n, a(n) for n=1..80.

Formula

(See the Mathematica code.)

a(n) = n+m-3 if 2*n <= (m-2)*(m+3) and a(n) = n+m-2 otherwise, where m = floor(sqrt(8*n+25)/2). - Chai Wah Wu, Nov 05 2025

Mathematica

a=1/2; b=7/2;
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}]

Prog

(PARI) a(n)=n-1+ceil(sqrt(8*n+25)/2-5/2) \\ Charles R Greathouse IV, Jan 20 2016
(Python)
from math import isqrt
def A183292(n): return n-3+(m:=isqrt((n<<3)+25)>>1)+((n<<1)>(m-2)*(m+3)) # Chai Wah Wu, Nov 05 2025

Crossrefs

Cf. A055999.

Sequence in context: A028968 A029598 A184004 * A039193 A028798 A138309

Adjacent sequences: A183289 A183290 A183291 * A183293 A183294 A183295

Keyword

nonn

Author

Clark Kimberling, Jan 03 2011

Status

approved