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A255773
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Tree of lower Wythoff numbers (A000201) generated as the 1-component of the graph described at A095903.
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4
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1, 3, 4, 6, 8, 9, 12, 11, 14, 16, 21, 17, 22, 25, 33, 19, 24, 27, 35, 29, 37, 42, 55, 30, 38, 43, 56, 46, 59, 67, 88, 32, 40, 45, 58, 48, 61, 69, 90, 50, 63, 71, 92, 76, 97, 110, 144, 51, 64, 72, 93, 77, 98, 111, 145, 80, 101, 114, 148, 122, 156, 177, 232
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OFFSET
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1,2
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COMMENTS
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This sequence and A255774 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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