16,807

← 16806 16807 16808 →
Cardinalsixteen thousand eight hundred seven
Ordinal16807th
(sixteen thousand eight hundred seventh)
Factorization75
Greek numeral͵Ϛωζ´
Roman numeralXVMDCCCVII, xvmdcccvii
Binary1000001101001112
Ternary2120011113
Senary2054516
Octal406478
Duodecimal988712
Hexadecimal41A716

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

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A000272 (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.
allikas: https://en.wikipedia.org/wiki/16,807