A183225 Array: row r is the complement of the (r+2)-gonal numbers; by antidiagonals.

2, 4, 2, 5, 3, 2, 7, 5, 3, 2, 8, 6, 4, 3, 2, 9, 7, 6, 4, 3, 2, 11, 8, 7, 5, 4, 3, 2, 12, 10, 8, 7, 5, 4, 3, 2, 13, 11, 9, 8, 6, 5, 4, 3, 2, 14, 12, 10, 9, 8, 6, 5, 4, 3, 2, 16, 13, 11, 10, 9, 7, 6, 5, 4, 3, 2, 17, 14, 13, 11, 10, 9, 7, 6, 5, 4, 3, 2, 18

Offset: 1

Author

Clark Kimberling, Jan 01 2011

Keywords

• nonn
• tabl

Comments

The n-th non k-gonal number is given by n+round(sqrt(2n/(k-2))) for k <= 10 and given by n+round(sqrt((2n-2+floor((k+1)/4))/(k-2))) for k > 10. - Chai Wah Wu, Oct 06 2024

Examples

			Northwest corner:
2...4...5...7...8...9...11...12...13 (A014132)
2...3...5...6...7...8...10...11...12 (A000037)
2...3...4...6...7...8....9...10...11 (A183217)
2...3...4...5...7...8....9...10...11 (A183218)
2...3...4...5...6...8....9...10...11 (A183219)
2...3...4...5...6...7....9...10...11 (A183220)
2...3...4...5...6...7....8...10...11 (A183221)
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086270 (array of the r-gonal numbers by rows),

A014132 (complement of the triangular numbers),

A000037 (complement of the squares),

A183217 (complement of the pentagonal numbers).

Programs

Python

from itertools import count, islice
from math import isqrt
def A183225_T(n,k): return n+(isqrt(((n<<3)+(-8+(k+1&-4) if k>10 else 0))//(k-2))+1>>1)
def A183225_gen(): # generator of terms
    return (A183225_T(m-k+3,k) for m in count(1) for k in range(3,m+3))
A183225_list = list(islice(A183225_gen(),100)) # Chai Wah Wu, Oct 06 2024