A329230 The number of steps it takes to reach all n positions around a circle during the grasshopper procedure.
1, 2, 3, 4, 10, 9, 7, 8, 23, 17, 16, 21, 20, 27, 29, 16, 58, 25, 28, 30, 40, 43, 88, 50, 40, 55, 87, 50, 62, 59, 70, 32, 81, 72, 67, 91, 84, 73, 71, 125, 107, 113, 69, 88, 148, 116, 135, 113, 158, 95, 137, 114, 182, 123, 174, 166, 112, 146, 215, 173, 126, 171
Offset: 1
Examples
For n = 5 the a(5) = 10 steps are: [0,0,0,0,0] (randomly step to first position) [1,0,0,0,0] (length 1 clockwise (right) step) [1,1,0,0,0] (length 2 clockwise (right) step) [1,1,0,1,0] (length 3 clockwise (right) step) [1,2,0,1,0] (length 4 counterclockwise (left) step) [1,2,1,1,0] (length 5 clockwise (right) step) [1,2,2,1,0] (length 6 clockwise (right) step) [1,2,2,2,0] (length 7 clockwise (right) step) [2,2,2,2,0] (length 8 clockwise (right) step) [2,2,2,3,0] (length 9 counterclockwise (left) step) [2,2,2,3,1] For example, the length 4 counterclockwise step occurs because stepping clockwise would result in landing in a position which has been visited once, and stepping counterclockwise would result in landing in a position which has not been visited before.
Links
- Peter Kagey, Table of n, a(n) for n = 1..5000
- Mathematics Stack Exchange User Vepir, Grasshopper jumping on circles.
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