There exists an integer such that every string in the look and say sequence "decays" in at most days to a compound of "common" and "transuranic elements."
The table below gives the periodic table of atoms associated with the look and say sequence as named by Conway (1987). The "abundance" is the average number of occurrences for long strings out of every million atoms. The asymptotic abundances are zero for transuranic elements, and 27.246... for arsenic (As), the next rarest element. The most common element is hydrogen (H), having an abundance of . The starting element is U, represented by the string "3," and subsequent terms are those giving a description of the current term: one three (13); one one, one three (1113); three ones, one three (3113), etc.
abundance | is the derivate of | ||
102.56285249 | 92 | U | 3 |
9883.5986392 | 91 | Pa | 13 |
7581.9047125 | 90 | Th | 1113 |
6926.9352045 | 89 | Ac | 3113 |
5313.7894999 | 88 | Ra | 132113 |
4076.3134078 | 87 | Fr | 1113122113 |
3127.0209328 | 86 | Rn | 311311222113 |
2398.7998311 | 85 | At | Ho.1322113 |
1840.1669683 | 84 | Po | 1113222113 |
1411.6286100 | 83 | Bi | 3113322113 |
1082.8883285 | 82 | Pb | Pm.123222113 |
830.70513293 | 81 | Tl | 111213322113 |
637.25039755 | 80 | Hg | 31121123222113 |
488.84742982 | 79 | Au | 132112211213322113 |
375.00456738 | 78 | Pt | 111312212221121123222113 |
287.67344775 | 77 | Ir | 3113112211322112211213322113 |
220.68001229 | 76 | Os | 1321132122211322212221121123222113 |
169.28801808 | 75 | Re | 111312211312113221133211322112211213322113 |
315.56655252 | 74 | W | Ge.Ca.312211322212221121123222113 |
242.07736666 | 73 | Ta | 13112221133211322112211213322113 |
2669.0970363 | 72 | Hf | 11132.Pa.H.Ca.W |
2047.5173200 | 71 | Lu | 311312 |
1570.6911808 | 70 | Yb | 1321131112 |
1204.9083841 | 69 | Tm | 11131221133112 |
1098.5955997 | 68 | Er | 311311222.Ca.Co |
47987.529438 | 67 | Ho | 1321132.Pm |
36812.186418 | 66 | Dy | 111312211312 |
28239.358949 | 65 | Tb | 3113112221131112 |
21662.972821 | 64 | Gd | Ho.13221133112 |
20085.668709 | 63 | Eu | 1113222.Ca.Co |
15408.115182 | 62 | Sm | 311332 |
29820.456167 | 61 | Pm | 132.Ca.Zn |
22875.863883 | 60 | Nd | 111312 |
17548.529287 | 59 | Pr | 31131112 |
13461.825166 | 58 | Ce | 1321133112 |
10326.833312 | 57 | La | 11131.H.Ca.Co |
7921.9188284 | 56 | Ba | 311311 |
6077.0611889 | 55 | Cs | 13211321 |
4661.8342720 | 54 | Xe | 11131221131211 |
3576.1856107 | 53 | I | 311311222113111221 |
2743.3629718 | 52 | Te | Ho.1322113312211 |
2104.4881933 | 51 | Sb | Eu.Ca.3112221 |
1614.3946687 | 50 | Sn | Pm.13211 |
1238.4341972 | 49 | In | 11131221 |
950.02745646 | 48 | Cd | 3113112211 |
728.78492056 | 47 | Ag | 132113212221 |
559.06537946 | 46 | Pd | 111312211312113211 |
428.87015041 | 45 | Rh | 311311222113111221131221 |
328.99480576 | 44 | Ru | Ho.132211331222113112211 |
386.07704943 | 43 | Tc | Eu.Ca.311322113212221 |
296.16736852 | 42 | Mo | 13211322211312113211 |
227.19586752 | 41 | Nb | 1113122113322113111221131221 |
174.28645997 | 40 | Zr | Er.12322211331222113112211 |
133.69860315 | 39 | Y | 1112133.H.Ca.Tc |
102.56285249 | 38 | Sr | 3112112.U |
78.678000089 | 37 | Rb | 1321122112 |
60.355455682 | 36 | Kr | 11131221222112 |
46.299868152 | 35 | Br | 3113112211322112 |
35.517547944 | 34 | Se | 13211321222113222112 |
27.246216076 | 33 | As | 11131221131211322113322112 |
1887.4372276 | 32 | Ge | 31131122211311122113222.Na |
1447.8905642 | 31 | Ga | Ho.13221133122211332 |
23571.391336 | 30 | Zn | Eu.Ca.Ac.H.Ca.312 |
18082.082203 | 29 | Cu | 131112 |
13871.123200 | 28 | Ni | 11133112 |
45645.877256 | 27 | Co | Zn.32112 |
35015.858546 | 26 | Fe | 13122112 |
26861.360180 | 25 | Mn | 111311222112 |
20605.882611 | 24 | Cr | 31132.Si |
15807.181592 | 23 | V | 13211312 |
12126.002783 | 22 | Ti | 11131221131112 |
9302.0974443 | 21 | Sc | 3113112221133112 |
56072.543129 | 20 | Ca | Ho.Pa.H.12.Co |
43014.360913 | 19 | K | 1112 |
32997.170122 | 18 | Ar | 3112 |
25312.784218 | 17 | Cl | 132112 |
19417.939250 | 16 | S | 1113122112 |
14895.886658 | 15 | P | 311311222112 |
32032.812960 | 14 | Si | Ho.1322112 |
24573.006696 | 13 | Al | 1113222112 |
18850.441228 | 12 | Mg | 3113322112 |
14481.448773 | 11 | Na | Pm.123222112 |
11109.006696 | 10 | Ne | 111213322112 |
8521.9396539 | 9 | F | 31121123222112 |
6537.3490750 | 8 | O | 132112211213322112 |
5014.9302464 | 7 | N | 111312212221121123222112 |
3847.0525419 | 6 | C | 3113112211322112211213322112 |
2951.1503716 | 5 | B | 1321132122211322212221121123222112 |
2263.8860325 | 4 | Be | 111312211312113221133211322112211213322112 |
4220.0665982 | 3 | Li | Ge.Ca.312211322212221121123222112 |
3237.2968588 | 2 | He | 13112221133211322112211213322112 |
91790.383216 | 1 | H | Hf.Pa.22.Ca.Li |