Centered octagonal number
- Centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers. The centered octagonal number for "n" is given by the formula
:
where "T" is a regular triangular number, or much more simply, by squaring the odd numbers:
:
The first few centered octagonal numbers are
1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089
All centered octagonal numbers are odd, and in base 10 one can notice the one's digits follow the pattern 1-9-5-9-1.
Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number.
See also regular octagonal number.
Wikimedia Foundation.
2010.
Look at other dictionaries:
Centered polygonal number — The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. Each side of a polygonal layer contains one dot more than a side in the… … Wikipedia
Octagonal number — An octagonal number is a figurate number that represents an octagon. The octagonal number for n is given by the formula 3n2 2n, with n > 0. The first few octagonal numbers are: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645 … Wikipedia
1000 (number) — List of numbers Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k → Cardinal 1000 one thousand … Wikipedia
3000 (number) — 3000 (three thousand) is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English (when and is required from 101 forward). In other fields In the novel The Brothers Karamazov by Fyodor… … Wikipedia
2000 (number) — 2000 (two thousand) is the natural number following 1999 and preceding 2001.See also: millennium, year 2000 AD, Y2K, 2000 (disambiguation).Two thousand is the highest number expressible using only two unmodified characters in roman numerals… … Wikipedia
5000 (number) — 5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the English language. Selected numbers in the range 5001 5999 * 5003 Sophie Germain prime * 5020 amicable number with… … Wikipedia
400 (number) — ← 399 401 → 400 List of numbers Integers ← 0 100 200 … Wikipedia
4000 (number) — 4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number. Selected numbers in the range 4001 4999 * 4005 triangular number * 4007 safe prime * 4010 magic constant of n times; n normal magic square and … Wikipedia
6000 (number) — 6000 (six thousand) is the natural number following 5999 and preceding 6001. Selected numbers in the range 6001 6999 * 6025 Rhythm guitarist of the Dead Kennedys from June 1978 to March 1979. Full name is Carlos Cadona. * 6028 centered heptagonal … Wikipedia
7000 (number) — 7000 (seven thousand) is the natural number following 6999 and preceding 7001. Selected numbers in the range 7001 7999 * 7021 triangular number * 7043 Sophie Germain prime * 7056 84^2 * 7057 cuban prime of the form x = y + 1 * 7073 Leyland number … Wikipedia
