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In a certain number, one counts as follows: 1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 111, ...

 

What is the 54th symbol?

 May 20, 2020
 #1
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The 54th term = 1,223

 
 May 20, 2020
 #2
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>>> What is the 54th symbol? <<<

 

Xenon is the 54th element, and its symbol is Xe

 
 May 21, 2020
 #3
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In a certain number, one counts as follows: \(1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 111, \ldots\)

 

I assume: all numbers on base 4 without zeros in the numbers.

 

\(\begin{array}{|r|r|r|} \hline n_{10} & n_{4} & \text{count} \\ \hline 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3 \\ 4 & \color{lightgrey}10 \\ 5 & 11 & 4 \\ 6 & 12 & 5 \\ 7 & 13 & 6 \\ 8 & \color{lightgrey}20 \\ 9 & 21 & 7 \\ 10 & 22 & 8 \\ 11 & 23 & 9 \\ 12 & \color{lightgrey}30 \\ 13 & 31 & 10 \\ 14 & 32 & 11 \\ 15 & 33 & 12 \\ 16 & \color{lightgrey}100 \\ 17 & \color{lightgrey}101 \\ 18 & \color{lightgrey}102 \\ 19 & \color{lightgrey}103 \\ 20 & \color{lightgrey}110 \\ 21 & 111 & 13 \\ 22 & 112 & 14 \\ 23 & 113 & 15 \\ 24 & \color{lightgrey}120 \\ 25 & 121 & 16 \\ 26 & 122 & 17 \\ 27 & 123 & 18 \\ 28 & \color{lightgrey}130 \\ 29 & 131 & 19 \\ 30 & 132 & 20 \\ 31 & 133 & 21 \\ 32 & \color{lightgrey}200 \\ 33 & \color{lightgrey}201 \\ 34 & \color{lightgrey}202 \\ 35 & \color{lightgrey}203 \\ 36 & \color{lightgrey}210 \\ 37 & 211 & 22 \\ 38 & 212 & 23 \\ 39 & 213 & 24 \\ 40 & \color{lightgrey}220 \\ 41 & 221 & 25 \\ 42 & 222 & 26 \\ 43 & 223 & 27 \\ 44 & \color{lightgrey}230 \\ 45 & 231 & 28 \\ 46 & 232 & 29 \\ 47 & 233 & 30 \\ \hline \end{array} \begin{array}{|r|r|r|} \hline n_{10} & n_{4} & \text{count} \\ \hline 48 & \color{lightgrey}300 \\ 49 & \color{lightgrey}301 \\ 50 & \color{lightgrey}302 \\ 51 & \color{lightgrey}303 \\ 52 & \color{lightgrey}310 \\ 53 & 311 & 31 \\ 54 & 312 & 32 \\ 55 & 313 & 33 \\ 56 & \color{lightgrey}320 \\ 57 & 321 & 34 \\ 58 & 322 & 35 \\ 59 & 323 & 36 \\ 60 & \color{lightgrey}330 \\ 61 & 331 & 37 \\ 62 & 332 & 38 \\ 63 & 333 & 39 \\ 64 & \color{lightgrey}1000 \\ 65 & \color{lightgrey}1001 \\ 66 & \color{lightgrey}1002 \\ 67 & \color{lightgrey}1003 \\ 68 & \color{lightgrey}1010 \\ 69 & \color{lightgrey}1011 \\ 70 & \color{lightgrey}1012 \\ 71 & \color{lightgrey}1013 \\ 72 & \color{lightgrey}1020 \\ 73 & \color{lightgrey}1021 \\ 74 & \color{lightgrey}1022 \\ 75 & \color{lightgrey}1023 \\ 76 & \color{lightgrey}1030 \\ 77 & \color{lightgrey}1031 \\ 78 & \color{lightgrey}1032 \\ 79 & \color{lightgrey}1033 \\ 80 & \color{lightgrey}1100 \\ 81 & \color{lightgrey}1101 \\ 82 & \color{lightgrey}1102 \\ 83 & \color{lightgrey}1103 \\ 84 & \color{lightgrey}1110 \\ 85 & 1111 & 40 \\ 86 & 1112 & 41 \\ 87 & 1113 & 42 \\ 88 & \color{lightgrey}1120 \\ 89 & 1121 & 43 \\ 90 & 1122 & 44 \\ 91 & 1123 & 45 \\ 92 & \color{lightgrey}1130 \\ 93 & 1131 & 46 \\ 94 & 1132 & 47 \\ 95 & 1133 & 48 \\ 96 & \color{lightgrey}1200 \\ 97 & \color{lightgrey}1201 \\ 98 & \color{lightgrey}1202 \\ 99 & \color{lightgrey}1203 \\ 100 & \color{lightgrey}1210 \\ 101 & 1211 & 49 \\ 102 & 1212 & 50 \\ 103 & 1213 & 51 \\ 104 & \color{lightgrey}1220 \\ 105 & 1221 & 52 \\ 106 & 1222 & 53 \\ 107 & \color{red}1223 & \color{red}54 \\ \hline \end{array}\)

 

laugh

 
 May 21, 2020

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