16,807

← 16806 16807 16808 →
List of numbers Integers ← 0 10k 20k 30k 40k 50k 60k 70k 80k 90k →
Cardinal	sixteen thousand eight hundred seven
Ordinal	16807th (sixteen thousand eight hundred seventh)
Factorization	75
Greek numeral	${\displaystyle {\stackrel {\alpha }{\mathrm {M} }}}$͵Ϛωζ´
Roman numeral	XVMDCCCVII, xvmdcccvii
Binary	1000001101001112
Ternary	2120011113
Senary	2054516
Octal	406478
Duodecimal	988712
Hexadecimal	41A716

16807 is the natural number following 16806 and preceding 16808.

In mathematics

As a number of the form ${\displaystyle n^{n-2}}$ (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 ${\displaystyle 7^{4}}$ kittens, but reaching one more step, ${\displaystyle 7^{5}=16807}$ 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]}

${\displaystyle X_{k+1}=16807\cdot X_{k}~~{\bmod {~}}~2147483647}$

References

1. Sloane, N. J. A. (ed.). "SequenceA000272(Number of trees on n labeled nodes: n^(n-2))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Aldous, Joan M.; Wilson, Robin J. (2003). Graphs and Applications: An Introductory Approach. Springer Science & Business Media. pp.  164–165. ISBN   9781852332594.
3. Maor, Eli (2002) [1988]. "Recreational Mathematics in Ancient Egypt" (PDF). Trigonometric Delights. Princeton University Press. pp. 11–14 (in PDF, 1–4). ISBN   978-0-691-09541-7. Archived from the original (PDF) on 2005-12-24. Retrieved 2009-04-19.
4. Gardner, Bob (August 13, 2023). "2.10. Egypt: A Curious Problem in the Rhind Papyrus" (PDF). History of Mathematics before 1600 - Class Notes. East Tennessee State University. Retrieved 2025-12-13.
5. 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.
6. Schrage, Linus (1979). "A More Portable Fortran Random Number Generator". ACM Transactions on Mathematical Software. 5 (2): 132–138. CiteSeerX   10.1.1.470.6958 . doi:10.1145/355826.355828. S2CID   14090729.
7. Park, S.K.; Miller, K.W. (1988). "Random Number Generators: Good Ones Are Hard To Find" (PDF). Communications of the ACM . 31 (10): 1192–1201. doi:10.1145/63039.63042. S2CID   207575300.

External links

• 16807 : facts & properties