Recursively Rotated Possible Permutation
Leroy Quet
qq-quet at mindspring.com
Thu Sep 9 15:34:22 CEST 2004
Hugo Pfoertner wrote:
>Leroy Quet wrote:
>>
>> I just submitted the following sequence to the EIS.
>>
>> %S A000001 1,3,4,2,7,8,6,11,12
>> %N A000001 Start with positive integers. On m_th step shift terms a(m+1)
>> to a(2m-1) one position to the left, move a(m) to position (2m-1).
>> Sequence is limit of reordering.
>> %e A000001 [1,2,3,4,5,6,...]->[1,3,2,4,5,6,...]->[1,3,4,5,2,6,...]
>> ->[1,3,4,2,6,7,...]->[1,3,4,2,7,5,...]->[1,3,4,2,7,8,...]
>> ->...
>> %O A000001 1
>> %K A000001 ,more,nonn,
>>
>> Is it a permutation of the positive integers?
>> (Or do some integers get rotated out to infinity?)
>>
>> I bet there is a simple, even trivial, way to express which integer is at
>> any particular position. (But a maybe not.)
>>
>> Could someone please extend this sequence once it appears, and if it is a
>> permutation, submit the inverse?
>>
>> thanks,
>> Leroy Quet
>
>I get (15 numbers / line, revealing a nice structure):
>
> 1 3 4 2 7 8 6 11 12 9 15 16 5 19 20
> 14 23 24 17 27 28 13 31 32 22 35 36 25 39 40
> 18 43 44 30 47 48 33 51 52 10 55 56 38 59 60
> 41 63 64 29 67 68 46 71 72 49 75 76 34 79 80
> 54 83 84 57 87 88 26 91 92 62 95 96 65 99 100
> 45 103 104 70 107 108 73 111 112 50 115 116 78 119 120
> 81 123 124 37 127 128 86 131 132 89 135 136 61 139 140
> 94 143 144 97 147 148 66 151 152 102 155 156 105 159 160
> 21 163 164 110 167 168 113 171 172 77 175 176 118 179 180
>121 183 184 82 187 188 126 191 192 129 195 196 58 199 200
>
>and the inverse
>
> 1 4 2 3 13 7 5 6 10 40 8 9 22 16 11
> 12 19 31 14 15 121 25 17 18 28 67 20 21 49 34
> 23 24 37 58 26 27 94 43 29 30 46 364 32 33 76
> 52 35 36 55 85 38 39 202 61 41 42 64 148 44 45
>103 70 47 48 73 112 50 51 175 79 53 54 82 283 56
> 57 130 88 59 60 91 139 62 63 1093 97 65 66 100 229
> 68 69 157 106 71 72 109 166 74 75 256 115 77 78 118
>607 80 81 184 124 83 84 127 193 86 87 445 133 89 90
>136 310 92 93 211 142 95 96 145 220 98 99 337 151 101
>102 154 526 104 105 238 160 107 108 163 247 110 111 850 169
>
>Hugo Pfoertner
Hmmm... I wonder now about any patterns when the sequence is taken mod m
(for other m's besides 10).
thanks,
Leroy Quet
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