16,807
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | sixteen thousand eight hundred seven | |||
| Ordinal | 16807th (sixteen thousand eight hundred seventh) | |||
| Factorization | 75 | |||
| Greek numeral | ͵Ϛωζ´ | |||
| Roman numeral | XVMDCCCVII | |||
| Binary | 1000001101001112 | |||
| Ternary | 2120011113 | |||
| Quaternary | 100122134 | |||
| Quinary | 10142125 | |||
| Senary | 2054516 | |||
| Octal | 406478 | |||
| Duodecimal | 988712 | |||
| Hexadecimal | 41A716 | |||
| Vigesimal | 220720 | |||
| Base 36 | CYV36 | |||
16807 is the natural number following 16806 and preceding 16808.
In mathematics
As a number of the form (16807 = 75), it can be applied in Cayley's formula to count the number of trees with seven labeled nodes.[1][2]
The powers of seven, including this one, feature in problem 79 from the Rhind Mathematical Papyrus, from ancient Egypt circa 1650 BC. It resembles the modern English riddle As I was going to St Ives, which compounds powers of seven up to kittens, but reaching one more step, hekat (an ancient Egyptian unit of measurement for grain).[3] Another puzzle of the same type, with 16807 knives, occurs in Fibonacci's Liber Abaci.[4]
In other fields
- Several authors have suggested a Lehmer random number generator:[5][6][7]
References
- ↑ Sloane, N. J. A., ed. "Sequence A000272 (Number of trees on n labeled nodes: n^(n-2))". OEIS Foundation. https://oeis.org/A000272.
- ↑ Aldous, Joan M.; Wilson, Robin J. (2003). Graphs and Applications: An Introductory Approach. Springer Science & Business Media. pp. 164–165. ISBN 9781852332594.
- ↑ Maor, Eli (2002). "Recreational Mathematics in Ancient Egypt". Trigonometric Delights. Princeton University Press. pp. 11–14 (in PDF, 1–4). ISBN 978-0-691-09541-7. http://pup.princeton.edu/books/maor/sidebar_a.pdf. Retrieved 2009-04-19.
- ↑ Gardner, Bob (August 13, 2023). "2.10. Egypt: A Curious Problem in the Rhind Papyrus". History of Mathematics before 1600 - Class Notes. East Tennessee State University. https://faculty.etsu.edu/gardnerr/3040/Notes-Eves6/Eves6-2-10.pdf.
- ↑ Lewis, P.A.W.; Goodman A.S.; Miller J.M. (1969). "A pseudo-random number generator for the system/360". IBM Systems Journal 8 (2): 136–143. doi:10.1147/sj.82.0136.
- ↑ Schrage, Linus (1979). "A More Portable Fortran Random Number Generator". ACM Transactions on Mathematical Software 5 (2): 132–138. doi:10.1145/355826.355828.
- ↑ Park, S.K.; Miller, K.W. (1988). "Random Number Generators: Good Ones Are Hard To Find". Communications of the ACM 31 (10): 1192–1201. doi:10.1145/63039.63042. http://www.firstpr.com.au/dsp/rand31/p1192-park.pdf.
External links
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