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{{Infobox number
{{Infobox number
| number = 900009
| number = 90000}}
}}


'''90,000''' ('''ninety thousand''') is the [[natural number]] following [[80,000#Selected numbers in the range 80,000–89,999|89,999]] and preceding 90,001. It is the sum of the cubes of the first 24 positive integers, and is the square of 300.
'''90,000''' ('''ninety thousand''') is the [[natural number]] following [[80,000#Selected numbers in the range 80,000–89,999|89,999]] and preceding 90,001. It is the sum of the cubes of the first 24 positive integers, and is the square of 300.
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* '''90,625''' = the only five-digit [[automorphic number]]: 90625<sup>2</sup> = 8212890625<ref>{{Cite web|url=https://oeis.org/A003226|title=Sloane's A003226 : Automorphic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''90,625''' = the only five-digit [[automorphic number]]: 90625<sup>2</sup> = 8212890625<ref>{{Cite web|url=https://oeis.org/A003226|title=Sloane's A003226 : Automorphic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''91,125''' = 45<sup>3</sup>
* '''91,125''' = 45<sup>3</sup>
* '''91,144''' = Fine number<ref>{{cite OEIS|A000957|Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree|access-date=2022-06-01}}</ref>
* '''91,144''' = Fine number{{huh|date=March 2024}}<ref>{{cite OEIS|A000957|Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree|access-date=2022-06-01}}</ref>
* '''92,205''' = number of 23-bead necklaces (turning over is allowed) where complements are equivalent<ref>{{cite OEIS|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
* '''92,706''' = There is a math puzzle called KAYAK + KAYAK + KAYAK + KAYAK + KAYAK + KAYAK = SPORT, where each letter represents a digit. When one solves the puzzle, KAYAK = 15451, and when one added this up, SPORT = 92,706. <ref>{{cite web | url=https://www.mathsisfun.com/puzzles/kayak-solution.html | title=KAYAK Puzzle - Solution }}</ref>
* '''93,312''' = [[Leyland number]]: 6<sup>6</sup> + 6<sup>6</sup>.<ref name=":0">{{Cite web|url=https://oeis.org/A076980|title=Sloane's A076980 : Leyland numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref> Also a 3-smooth number.
* '''93,312''' = [[Leyland number]]: 6<sup>6</sup> + 6<sup>6</sup>.<ref name=":0">{{Cite web|url=https://oeis.org/A076980|title=Sloane's A076980 : Leyland numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref> Also a 3-smooth number.
* '''94,249''' = [[palindromic number|palindromic]] square: 307<sup>2</sup>
* '''94,249''' = [[palindromic number|palindromic]] square: 307<sup>2</sup>
* '''94,932''' = Leyland number: 7<sup>5</sup> + 5<sup>7</sup><ref name=":0" />
* '''94,932''' = Leyland number: 7<sup>5</sup> + 5<sup>7</sup><ref name=":0" />
* '''95,121''' = [[Kaprekar number]]: 95121<sup>2</sup> = 9048004641; 90480 + 04641 = 95121<ref name=":1">{{Cite web|url=https://oeis.org/A006886|title=Sloane's A006886 : Kaprekar numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''95,121''' = [[Kaprekar number]]: 95121<sup>2</sup> = 9048004641; 90480 + 04641 = 95121<ref name=":1">{{Cite web|url=https://oeis.org/A006886|title=Sloane's A006886 : Kaprekar numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''95,420''' = number of 22-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref>{{cite OEIS|A000013|Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed}}</ref>
* '''96,557''' = [[Markov number]]: 5<sup>2</sup> + 6466<sup>2</sup> + 96557<sup>2</sup> = 3 × 5 × 6466 × 96557<ref>{{Cite web|url=https://oeis.org/A002559|title=Sloane's A002559 : Markoff (or Markov) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''96,557''' = [[Markov number]]: 5<sup>2</sup> + 6466<sup>2</sup> + 96557<sup>2</sup> = 3 × 5 × 6466 × 96557<ref>{{Cite web|url=https://oeis.org/A002559|title=Sloane's A002559 : Markoff (or Markov) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-16}}</ref>
* '''97,336''' = 46<sup>3</sup>, the largest 5-digit cube
* '''97,336''' = 46<sup>3</sup>, the largest 5-digit cube
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* '''99,991''' = largest five-digit [[prime number]]
* '''99,991''' = largest five-digit [[prime number]]
* '''99,999''' = [[repdigit]], Kaprekar number: 99999<sup>2</sup> = 9999800001; 99998 + 00001 = 99999<ref name=":1" />
* '''99,999''' = [[repdigit]], Kaprekar number: 99999<sup>2</sup> = 9999800001; 99998 + 00001 = 99999<ref name=":1" />

===Primes===
There are 879 prime numbers between 90000 and 100000.


==References==
==References==
{{Reflist}}
{{Reflist}}

==External links==
* {{cci}}


{{Integers|10}}
{{Integers|10}}


[[Category:Integers|90000]]
[[Category:Integers|90000]]


{{num-stub}}

Latest revision as of 05:39, 17 September 2024

← 89999 90000 90001 →
Cardinalninety thousand
Ordinal90000th
(ninety thousandth)
Factorization24 × 32 × 54
Greek numeral
Roman numeralXC
Binary101011111100100002
Ternary111201101003
Senary15324006
Octal2576208
Duodecimal4410012
Hexadecimal15F9016

90,000 (ninety thousand) is the natural number following 89,999 and preceding 90,001. It is the sum of the cubes of the first 24 positive integers, and is the square of 300.

Selected numbers in the range 90,000–99,999

[edit]
  • 90,625 = the only five-digit automorphic number: 906252 = 8212890625[1]
  • 91,125 = 453
  • 91,144 = Fine number[clarification needed][2]
  • 92,205 = number of 23-bead necklaces (turning over is allowed) where complements are equivalent[3]
  • 92,706 = There is a math puzzle called KAYAK + KAYAK + KAYAK + KAYAK + KAYAK + KAYAK = SPORT, where each letter represents a digit. When one solves the puzzle, KAYAK = 15451, and when one added this up, SPORT = 92,706. [4]
  • 93,312 = Leyland number: 66 + 66.[5] Also a 3-smooth number.
  • 94,249 = palindromic square: 3072
  • 94,932 = Leyland number: 75 + 57[5]
  • 95,121 = Kaprekar number: 951212 = 9048004641; 90480 + 04641 = 95121[6]
  • 95,420 = number of 22-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[7]
  • 96,557 = Markov number: 52 + 64662 + 965572 = 3 × 5 × 6466 × 96557[8]
  • 97,336 = 463, the largest 5-digit cube
  • 98,304 = 3-smooth number
  • 99,066 = largest number whose square uses all of the decimal digits once: 990662 = 9814072356. It is also strobogrammatic in decimal.
  • 99,856 = 3162, the largest 5-digit square
  • 99,991 = largest five-digit prime number
  • 99,999 = repdigit, Kaprekar number: 999992 = 9999800001; 99998 + 00001 = 99999[6]

Primes

[edit]

There are 879 prime numbers between 90000 and 100000.

References

[edit]
  1. ^ "Sloane's A003226 : Automorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-16.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000957". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-01.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ "KAYAK Puzzle - Solution".
  5. ^ a b "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-16.
  6. ^ a b "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-16.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-16.
[edit]


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