22 (number)

Last updated
21 22 23
Cardinal twenty-two
Ordinal 22nd
(twenty-second)
Factorization 2 × 11
Divisors 1, 2, 11, 22
Greek numeral ΚΒ´
Roman numeral XXII, xxii
Binary 101102
Ternary 2113
Senary 346
Octal 268
Duodecimal 1A12
Hexadecimal 1616

22 (twenty-two) is the natural number following 21 and preceding 23.

Contents

In mathematics

22 is a semiprime, [1] a Smith number, and an Erdős–Woods number. [2] [3] is a commonly used approximation of the irrational number π, the ratio of the circumference of a circle to its diameter.

22 can read as "two twos", which is the only fixed point of John Conway's look-and-say function. [4]

The number 22 appears prominently within sporadic groups. The Mathieu group M22 is one of 26 sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points. [5] There are also 22 regular complex apeirohedra. [6]

22 has been proven to be a Lychrel number in base 2, [7] since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after 4n steps it reaches a number consisting of 10, followed by n + 1 ones, followed by 01, followed by n + 1 zeros. This number obviously cannot be a palindrome, and none of the other numbers in the sequence are palindromes.

In other fields

In culture and religion

In weights and measures

In other uses

Twenty-two may also refer to:

See also

References

  1. Sloane, N. J. A. (ed.). "SequenceA001358". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "SequenceA006753(Smith numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-31.
  3. Sloane, N. J. A. (ed.). "SequenceA059756(Erdős-Woods numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-31.
  4. Sloane, N. J. A. (ed.). "SequenceA010861(Look-and-say constant sequence 22)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-07-21.
  5. Weisstein, Eric W. "Mathieu Groups". mathworld.wolfram.com. Retrieved 2022-07-02.
  6. Coxeter, H.S.M. (1991), Regular Complex Polytopes, Cambridge University Press, p. 140, ISBN   0-521-39490-2
  7. Sloane, N. J. A. (ed.). "SequenceA060382". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. "Definition of CATCH-22". www.merriam-webster.com. Retrieved 2020-08-12.
  9. Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN   978-1-57324-560-9.
  10. "Definition of CHAIN". www.merriam-webster.com. Retrieved 2020-08-19. a unit of length equal to 66 feet
  11. Cuartas, Javier (1990-01-05). "La suerte de los dos patitos" [The luck of the two little ducks]. El País (in Spanish). Oviedo. Retrieved 17 September 2020.
  12. Sanz, Elena (26 April 2010). "Los dos patitos, la niña bonita, la mala pata..." Muy Interesante (in Spanish). Retrieved 17 September 2020. Lo más normal es que el nombre tuviera que ver con la forma del número. Por ejemplo, el 11 era las banderillas, y el 22, los dos patitos o las monjas arrodilladas.