A183217 Complement of the pentagonal numbers.

2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 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, 86, 87, 88, 89, 90, 91, 93

Offset: 1

Author

Clark Kimberling, Jan 01 2011

Keywords

• nonn
• easy

Examples

			The pentagonal numbers A000326 = (1,5,12,22,35,...), so that this sequence = (2,3,4,6,7,8,9,10,11,13,14,...).
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000326, A111651.

Programs

Mathematica

Table[n+Floor[1/2+(2n/3)^(1/2)], {n,100}]

PARI

a(n) = n + sqrtint(24*n)\/6; \\ Kevin Ryde, Aug 31 2024

Python

from math import isqrt
def A183217(n): return n+(isqrt((n<<3)//3)+1>>1) # Chai Wah Wu, Oct 05 2024

Formula

a(n) = n + floor(1/2+(2n/3)^(1/2)).

a(n) = n + A111651(n). - Kevin Ryde, Aug 31 2024