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A183219
Complement of the heptagonal (7-gonal) numbers.
2
2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
OFFSET
1,1
FORMULA
n+Floor[1/2+(2n/5)^(1/2)].
EXAMPLE
7-gonal numbers: (1,7,18,34,55,...)=A000566, so that
A183219=(2,3,4,5,6,8,9,...17,19,...33,35,...).
MATHEMATICA
Table[n+Floor[1/2+(2n/5)^(1/2)], {n, 100}]
Module[{nn=7, heps}, heps=PolygonalNumber[7, Range[nn]]; Complement[Range[Last[heps]], heps]] (* Harvey P. Dale, Apr 02 2023 *)
PROG
(Python)
from math import isqrt
def A183219(n): return n+(isqrt((n<<3)//5)+1>>1) # Chai Wah Wu, Oct 05 2024
CROSSREFS
Cf. A000566.
Sequence in context: A129618 A349536 A038673 * A049533 A052419 A257458
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 01 2011
STATUS
approved