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A245905
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Zero followed by the terms of A023705 arranged to give the unique path to the n-th node of a complete, rooted and ordered ternary tree.
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0
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0, 1, 2, 3, 5, 9, 13, 6, 10, 14, 7, 11, 15, 21, 37, 53, 25, 41, 57, 29, 45, 61, 22, 38, 54, 26, 42, 58, 30, 46, 62, 23, 39, 55, 27, 43, 59, 31, 47, 63, 85, 149, 213, 101, 165, 229, 117, 181, 245, 89, 153, 217, 105, 169, 233, 121, 185, 249, 93, 157, 221, 109, 173, 237, 125, 189, 253
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OFFSET
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1,3
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COMMENTS
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There is no path to the root node so first node path is 0. All other paths are represented by the terms of A023705 that are base 4 numbers containing no zeros. Starting at the lowest order digit base 4, if this is 1 then the path from the root node is to the left, if it is 2 straight on and if it is 3 to the right. Each successive digit order defines the next path to be taken until the highest digit order is reached and the specified node found.
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LINKS
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EXAMPLE
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a(33)=39, so the path to the 33rd node is given by 39 and when represented as the base 4 number gives 213. Hence the path to the 33rd node from the root node is Right, Left, Straight.
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MATHEMATICA
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tree=3; nest[{m2_, p2_}] := If[(mod=Mod[m2, tree])>1, (ind=mod-1; {(m2+tree-mod)/tree, ind+p2*(tree+1)}), (ind=tree+mod-1; {(m2-mod)/tree, ind+p2*(tree+1)})]; Table[NestWhile[nest, {n, 0}, #[[1]]!=1 &][[2]], {n, 1, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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