The Sixers sequence is a name that can be given to sequence A087409. I learned about this sequence in a Numberphile video, and it can be constructed as follows:
First, take the multiples of 6, written in base 10:
6, 12, 18, 24, 30, 36, ...
Next, concatenate the numbers into a stream of digits:
61218243036...
Finally, regroup the stream into pairs and interpret each as an integer:
61, 21, 82, 43, 3, ...
As we're grouping the numbers into pairs, the maximum number in the sequence will be 99, and it turns out that all non-negative integers less than 100 are represented in the sequence. This challenge is to find the index of the first instance of a number in the Sixers sequence.
Input
An integer in the range [0-99]
. You do not need to account for numbers outside this range, and your solution can have any behaviour if such an input is given.
Output
The index of the first occurrence of the input number in the Sixers sequence. This may be 0- or 1-indexed; please say which you are using in your answer.
Rules
- The procedure to generate the sequence noted in the introduction is for illustrative purposes only, you can use any method you like as long as the results are the same.
- You can submit full programs or functions.
- Any sensible methods of input and output are allowed.
- Standard loopholes are disallowed.
- Links to test your code online are recommended!
- This is code-golf, so shortest answer in each language wins!
Test cases
Here is a list of all input and outputs, in the format input, 0-indexed output, 1-indexed output
.
0 241 242
1 21 22
2 16 17
3 4 5
4 96 97
5 126 127
6 9 10
7 171 172
8 201 202
9 14 15
10 17 18
11 277 278
12 20 21
13 23 24
14 19 20
15 29 30
16 32 33
17 297 298
18 35 36
19 38 39
20 41 42
21 1 2
22 46 47
23 69 70
24 6 7
25 53 54
26 22 23
27 11 12
28 62 63
29 219 220
30 65 66
31 68 69
32 71 72
33 74 75
34 49 50
35 357 358
36 80 81
37 83 84
38 25 26
39 89 90
40 92 93
41 27 28
42 42 43
43 3 4
44 101 102
45 104 105
46 8 9
47 177 178
48 110 111
49 13 14
50 28 29
51 119 120
52 122 123
53 417 418
54 79 80
55 128 129
56 131 132
57 134 135
58 55 56
59 437 438
60 140 141
61 0 1
62 31 32
63 75 76
64 5 6
65 120 121
66 82 83
67 10 11
68 161 162
69 164 165
70 58 59
71 477 478
72 170 171
73 173 174
74 34 35
75 179 180
76 182 183
77 497 498
78 85 86
79 188 189
80 191 192
81 18 19
82 2 3
83 78 79
84 93 94
85 7 8
86 37 38
87 168 169
88 12 13
89 228 229
90 88 89
91 218 219
92 221 222
93 224 225
94 64 65
95 557 558
96 230 231
97 233 234
98 40 41
99 239 240
6, 2*6, 3*6,..., 325*6
is sufficient to generate all possible values \$\endgroup\$ – Luis Mendo Jun 14 '19 at 7:3700
,01
,02
, ...)? \$\endgroup\$ – Kevin Cruijssen Jun 14 '19 at 7:45