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

1,1

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000326, A111651.

Sequence in context: A048263 A141451 A285211 * A047303 A057906 A039214

Adjacent sequences: A183214 A183215 A183216 * A183218 A183219 A183220

Keyword

nonn,easy

Author

Clark Kimberling, Jan 01 2011

Status

approved