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A183220
Complement of the octagonal numbers.
3
2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
OFFSET
1,1
FORMULA
a(n) = n + floor(1/2+(n/3)^(1/2)).
EXAMPLE
Octagonal numbers: (1,8,21,40,65,...), so that we get (2,3,4,5,6,7,9,10,...,20,22,...,39,41...).
MATHEMATICA
Table[n+Floor[1/2+(n/3)^(1/2)], {n, 100}]
PROG
(Python)
from math import isqrt
def A183220(n): return n+(isqrt((n<<2)//3)+1>>1) # Chai Wah Wu, Oct 05 2024
CROSSREFS
Cf. A000567 (octagonal numbers).
Sequence in context: A369938 A138302 A270428 * A187947 A242094 A349144
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 01 2011
STATUS
approved