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宇宙學定理

存在一個 整數 N，使得 看說序列 中的每個字串在最多 N 天內“衰變”為“普通”和“超鈾元素”的混合物。

下表給出了與康威 (1987) 命名的 看說序列 相關的原子週期表。“丰度”是每百萬個原子中長字串的平均出現次數。超鈾元素的漸近丰度為零，而砷 (As) （下一種最稀有的元素）的漸近丰度為 27.246...。最常見的元素是氫 (H)，丰度為 91970.383...。起始元素是 U，用字串 “3” 表示，後續項是描述當前項的項：一個三 (13)；一個一，一個三 (1113)；三個一，一個三 (3113) 等。

丰度nE_nE_n 是 E_(n+1) 的導數
102.5628524992U3
9883.598639291Pa13
7581.904712590Th1113
6926.935204589Ac3113
5313.789499988Ra132113
4076.313407887Fr1113122113
3127.020932886Rn311311222113
2398.799831185AtHo.1322113
1840.166968384Po1113222113
1411.628610083Bi3113322113
1082.888328582PbPm.123222113
830.7051329381Tl111213322113
637.2503975580Hg31121123222113
488.8474298279Au132112211213322113
375.0045673878Pt111312212221121123222113
287.6734477577Ir3113112211322112211213322113
220.6800122976Os1321132122211322212221121123222113
169.2880180875Re111312211312113221133211322112211213322113
315.5665525274WGe.Ca.312211322212221121123222113
242.0773666673Ta13112221133211322112211213322113
2669.097036372Hf11132.Pa.H.Ca.W
2047.517320071Lu311312
1570.691180870Yb1321131112
1204.908384169Tm11131221133112
1098.595599768Er311311222.Ca.Co
47987.52943867Ho1321132.Pm
36812.18641866Dy111312211312
28239.35894965Tb3113112221131112
21662.97282164GdHo.13221133112
20085.66870963Eu1113222.Ca.Co
15408.11518262Sm311332
29820.45616761Pm132.Ca.Zn
22875.86388360Nd111312
17548.52928759Pr31131112
13461.82516658Ce1321133112
10326.83331257La11131.H.Ca.Co
7921.918828456Ba311311
6077.061188955Cs13211321
4661.834272054Xe11131221131211
3576.185610753I311311222113111221
2743.362971852TeHo.1322113312211
2104.488193351SbEu.Ca.3112221
1614.394668750SnPm.13211
1238.434197249In11131221
950.0274564648Cd3113112211
728.7849205647Ag132113212221
559.0653794646Pd111312211312113211
428.8701504145Rh311311222113111221131221
328.9948057644RuHo.132211331222113112211
386.0770494343TcEu.Ca.311322113212221
296.1673685242Mo13211322211312113211
227.1958675241Nb1113122113322113111221131221
174.2864599740ZrEr.12322211331222113112211
133.6986031539Y1112133.H.Ca.Tc
102.5628524938Sr3112112.U
78.67800008937Rb1321122112
60.35545568236Kr11131221222112
46.29986815235Br3113112211322112
35.51754794434Se13211321222113222112
27.24621607633As11131221131211322113322112
1887.437227632Ge31131122211311122113222.Na
1447.890564231GaHo.13221133122211332
23571.39133630ZnEu.Ca.Ac.H.Ca.312
18082.08220329Cu131112
13871.12320028Ni11133112
45645.87725627CoZn.32112
35015.85854626Fe13122112
26861.36018025Mn111311222112
20605.88261124Cr31132.Si
15807.18159223V13211312
12126.00278322Ti11131221131112
9302.097444321Sc3113112221133112
56072.54312920CaHo.Pa.H.12.Co
43014.36091319K1112
32997.17012218Ar3112
25312.78421817Cl132112
19417.93925016S1113122112
14895.88665815P311311222112
32032.81296014SiHo.1322112
24573.00669613Al1113222112
18850.44122812Mg3113322112
14481.44877311NaPm.123222112
11109.00669610Ne111213322112
8521.93965399F31121123222112
6537.34907508O132112211213322112
5014.93024647N111312212221121123222112
3847.05254196C3113112211322112211213322112
2951.15037165B1321132122211322212221121123222112
2263.88603254Be111312211312113221133211322112211213322112
4220.06659823LiGe.Ca.312211322212221121123222112
3237.29685882He13112221133211322112211213322112
91790.3832161HHf.Pa.22.Ca.Li

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康威常數, 看說序列

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參考文獻

Conway, J. H. "放射性衰變的怪異而奇妙的化學。" §5.11 in 通訊與計算中的未解決問題 (Ed. T. M. Cover and B. Gopinath). New York: Springer-Verlag, pp. 173-188, 1987.Conway, J. H. "放射性衰變的怪異而奇妙的化學。" Eureka, 5-18, 1985.Ekhad, S. B. and Zeilberger, D. "康威遺失的宇宙學定理的證明。" Electronic Research Announcement of the Amer. Math. Soc. 3, 78-82, 1997. http://www.math.temple.edu/~zeilberg/mamarim/mamarimhtml/horton.html.Hilgemeier, M. "Die Gleichniszahlen-Reihe." Bild der Wissensch. 12, 194-196, Dec. 1986.Hilgemeier, M. "'一個隱喻適合所有'：康威放射性衰變的分形之旅。" Ch. 7 in Pickover, C. A. (Ed.). 分形視界：分形的未來應用。 New York: St. Martin's Press, 1996.Wolfram, S. 一種新的科學。 Champaign, IL: Wolfram Media, p. 905, 2002.

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宇宙學定理

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Weisstein, Eric W. "宇宙學定理。" 來自 網路資源. https://mathworld.tw/CosmologicalTheorem.html

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