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A277214 a(n) is the Manhattan distance between n and 1 in a 3-dimensional cubic spiral of positive integers with 1..8 at the center (illustration in the comments). 0
0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 4, 5, 4, 3, 2, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Similar to A214526, but three-dimensional, and the core is 2 X 2 X 2 rather than 1 X 1.

The spiral begins as follows:

Level z=-2:

   95  94  93  92  91  90

   96  77  76  75  74  89

   97  78  67  66  73  88

   98  79  68  65  72  87

   99  80  69  70  71  86

  100  81  82  83  84  85

z=-1:

  116 115 114 113 112 111

  117  52  51  50  49 110

  118  53  62  61  60 109

  119  54  63  64  59 108

  120  55  56  57  58 107

  101 102 103 104 105 106

z=0:

  137 136 135 134 133 132

  138  39  38  37  48 131

  139  40   3   2  47 130

  140  41   4   1  46 129

  121  42  43  44  45 128

  122 123 124 125 126 127

z=1:

  144 145 146 147 148 149

  143  34  35  36  25 150

  142  33   6   7  26 151

  141  32   5   8  27 152

  160  31  30  29  28 153

  159 158 157 156 155 154

z=2:

  165 166 167 168 169 170

  164  21  22  23  24 171

  163  20  11  12  13 172

  162  19  10   9  14 173

  161  18  17  16  15 174

  180 179 178 177 176 175

z=3:

  186 187 188 189 190 191

  185 204 205 206 207 192

  184 203 214 215 208 193

  183 202 213 216 209 194

  182 201 212 211 210 195

  181 200 199 198 197 196

Algorithm sketch:

1. At every x-y plane the direction is clockwise if z > 0 and counterclockwise if z <= 0.

2. After an N*N cube is complete and we start building an M*M cube, M=N+2:

2a. The spiral at the first new edge of the M*M cube progresses from center to edges, in the same way as the A214526 spiral, e.g., z=-2 in the illustration.

2b. Between the first and last z-edges the spiral progresses according to item 1.

2c. The spiral at the last new edge of the M*M cube progresses from edges to center, e.g., z=3 in the illustration.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

abs( a(n) - a(n-1) ) = 1.

CROSSREFS

Cf. A214526.

Sequence in context: A043554 A005811 A008342 * A278603 A248218 A182110

Adjacent sequences:  A277211 A277212 A277213 * A277215 A277216 A277217

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Oct 05 2016

STATUS

approved

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Last modified April 12 09:29 EDT 2021. Contains 342920 sequences. (Running on oeis4.)