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A255774
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Tree of upper Wythoff numbers (A001950) generated as the 2-component of the graph described at A095903.
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5
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2, 5, 7, 10, 13, 15, 20, 18, 23, 26, 34, 28, 36, 41, 54, 31, 39, 44, 57, 47, 60, 68, 89, 49, 62, 70, 91, 75, 96, 109, 143, 52, 65, 73, 94, 78, 99, 112, 146, 81, 102, 115, 149, 123, 157, 178, 233, 83, 104, 117, 151, 125, 159, 180, 235, 130, 164, 185, 240, 198
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OFFSET
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1,1
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COMMENTS
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This sequence and A255773 partition the positive integers.
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LINKS
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EXAMPLE
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To generate the tree of lazy Fibonacci representations as in A095903, start with 1,2. Suffix the next two Fibonacci numbers, getting 1+2, 1+3; 2+3, 2+5. Suffix the next two Fibonacci numbers, getting 1+2+3, 1+2+5, 1+3+5, 1+3+8; 2+3+5, 2+3+8, 2+5+8, 2+5+13. Continue forever. A255773 is the tree of numbers having root (initial summand) 1, and A255774 is the tree of numbers having root (initial summand) 2.
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MATHEMATICA
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width = 6; t = Map[Total, Fibonacci[Flatten[NestList[Flatten[Map[{Join[#, {Last[#] +1}], Join[#, {Last[#] + 2}]} &, #], 1] &, {{2}, {3}}, width], 1]]](*A095903*)
Map[t[[#]] &, Apply[Range, {2^Range[#] - 1, 3 2^(Range[#] - 1) - 2}]] &[width + 1] (*A255773*)
Map[t[[#]] &, Apply[Range, {3 2^(Range[#] - 1) - 1, 2 (2^Range[#] - 1)}]] &[width + 1] (*A255774*) (* Peter J. C. Moses, Mar 06 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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