A183218 Complement of the hexagonal numbers.

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n)=n+Floor[1/2+(n/2)^(1/2)].

Example

Hexagonal numbers: (1,6,15,28,45,...) = A000384,
so that A183218=(2,3,4,5,7,8,9,...,14,16,...,27,29,...).

Mathematica

Table[n+Floor[1/2+(n/2)^(1/2)], {n, 100}]
Module[{nn=110}, Complement[Range[nn], PolygonalNumber[6, Range[ Floor[ (1+Sqrt[ 1+8nn])/4]]]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2020 *)

Prog

(Python)
from math import isqrt
def A183218(n): return n+(isqrt(n<<1)+1>>1) # Chai Wah Wu, Aug 26 2024

Crossrefs

Cf. A000384.

Sequence in context: A052414 A095410 A022293 * A071000 A088451 A047595

Adjacent sequences: A183215 A183216 A183217 * A183219 A183220 A183221

Keyword

nonn

Author

Clark Kimberling, Jan 01 2011

Status

approved