A183225 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

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

EXAMPLE

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)

PROG

(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

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).

Sequence in context: A307664 A057037 A076920 * A366586 A020774 A291303

Adjacent sequences: A183222 A183223 A183224 * A183226 A183227 A183228

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 01 2011

STATUS

approved