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Planus

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Planus is equal to [2] = 482 = 2,304 using PlantStar's Debut Notation.[1] The term was coined by PlantStar.

DeepLineMadom coined Inari Suomi for this number, and is the 30th number of the series Glycogenic Journey of the Britains.[2]

In sports[]

It is also the number of possible FIFA Confederations Cup outcomes (counting only group winners, runner-ups and knockout match winners) after the drawing of the final tournament.

Properties[]

2304 is a

  1. Square number [3]
  2. Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.[4]
  3. 3-smooth number: number of the form 2^i*3^j with i, j >= 0.[5]
  4. Half the number of 3 X n binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.[6]
  5. Sum of two distinct powers of 2.[7]
  6. number k of the form 2^i*3^j, where i and j >= 1.[8]
  7. Powerful number (A001694) that are not prime powers (A000961).[9]
  8. Jordan-Polya number: products of factorial number[10]
  9. Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.12.12 2D tiling[11]
  10. Number of normal semistandard Young tableaux whose shape is the integer partition with Heinz number n.[12]
  11. number that are divisible by exactly 10 primes with multiplicity.[13]
  12. Sum of twin prime pairs.[14]

Approximations[]

Notation Lower bound Upper bound
Scientific notation \(2.304\times10^3\)
Arrow notation \(48\uparrow2\)
Steinhaus-Moser Notation 4[3] 5[3]
Copy notation 2[4] 3[4]
Chained arrow notation \(48\rightarrow2\)
Taro's multivariable Ackermann function A(3,8) A(3,9)
Pound-Star Notation #*(2)*8 #*(2)*9
BEAF {48,2}
Hyper-E notation E[48]2
Bashicu matrix system (0)[47] (0)[48]
Hyperfactorial array notation 6! 7!
Bird's array notation {48,2}
Strong array notation s(48,2)
Fast-growing hierarchy \(f_2(8)\) \(f_2(9)\)
Hardy hierarchy \(H_{\omega^2}(8)\) \(H_{\omega^2}(9)\)
Slow-growing hierarchy \(g_{\omega^2}(48)\)

Sources[]

  1. ↑ Article 2.1: The Lineus Regiment | PlantStar's Large Numbers [dead link]
  2. ↑ Pointless Googolplex Stuffs - Glycogenic Journey of the Britains Retrieved 2025-02-22.
  3. ↑ https://oeis.org/A000290
  4. ↑ https://oeis.org/A000009
  5. ↑ https://oeis.org/A003586
  6. ↑ https://oeis.org/A069429
  7. ↑ https://oeis.org/A018900
  8. ↑ https://oeis.org/A033845
  9. ↑ https://oeis.org/A286708
  10. ↑ https://oeis.org/A001013
  11. ↑ https://oeis.org/A299257
  12. ↑ https://oeis.org/A296188
  13. ↑ https://oeis.org/A046314
  14. ↑ https://oeis.org/A054735

Lineus series: lineus · planus · spacus · tetrus · pentus · hexus · heptus · octus · nonus · decus · undecus · duodecus · tredecus · vigintus · trigintus · quadragintus
Lineans series: lineans · centus · millus · planans · spacans · tetrans · pentans · decans · vigintans · trigintans · quadragintans · lineduans · centans · planduans · spacduans · decduans · viginduans · linetrians · plantrians · spactrians · dectrians · linequadrans · planquadrans · decquadrans · linequintans · decquintans · linesextans · lineseptans · lineoctans · linenovans · linedecans · lineundecans · linedodecans · linetridecans · lineicosans · linetriacontans · linetetracontans
Enalineans series: enalineans · enaplanans · enaspacans · enadecans · enalineduans · enadecduans · enalinetrians · enalinedecans · enalineicosans · diolineans · dioplanans · diodecans · diolineduans · diolinetrians · diolinedecans · trialineans · triaplanans · trialineduans · trialinedecans · tesseralineans · tesseralineduans · pendelineans · exilineans · eptalineans · oktolineans · enealineans

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