A228853
Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
Original entry on oeis.org
1, 2, 3, 5, 7, 8, 11, 12, 13, 17, 18, 19, 21, 26, 27, 29, 30, 31, 34, 41, 43, 44, 45, 46, 47, 49, 50, 55, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 79, 80, 81, 89, 97, 99, 100, 101, 104, 105, 106, 108, 109, 111, 112, 115, 116, 117, 119, 121, 123, 128
Offset: 1
Part 1: Taking the first generation of edges of the tree to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5)}, which grows G(3) = {(3,5), (3,8), (5,7), (5,12)}, ... Expelling duplicate nodes and sorting leave {1, 2, 3, 5, 7, 8, ...}.
Part 2: The branch 2, 3, 8, 11, 19, 30, 49, 128, 305 has edge-labels 1, 2, 1, 1, 1, 1, 2, 2, so that 305/128 = [2, 2, 1, 1, 1, 1, 2, 1, 2].
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f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 1; y = 2; t = {{x, y}}; u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u]; w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]]; Sort[Union[w]]
A228854
Nodes of tree generated as follows: (1,3) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
Original entry on oeis.org
1, 3, 4, 7, 10, 11, 15, 17, 18, 24, 25, 26, 27, 29, 37, 40, 41, 43, 44, 47, 56, 58, 61, 63, 64, 65, 67, 68, 69, 71, 76, 89, 91, 93, 97, 98, 99, 100, 101, 104, 105, 106, 108, 109, 111, 112, 115, 123, 137, 138, 140, 147, 149, 152, 153, 154, 155, 157, 159, 160
Offset: 1
Taking the first generation of edges of the tree to be G(1) = {(1,3)}, the edge (1,3) grows G(2) = {(3,4), (3,7)}, which grows G(3) = {(4,7), (4,11), (7,10),(7,17)}, ... Expelling duplicate nodes and sorting leave {1,3,4,7,10,11,...}.
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f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 1; y = 3; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]
A228895
Nodes of tree generated as follows: (3,1) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
Original entry on oeis.org
1, 3, 4, 5, 6, 9, 11, 13, 14, 16, 17, 19, 22, 23, 27, 28, 31, 32, 33, 35, 37, 38, 39, 40, 43, 45, 47, 48, 51, 52, 53, 55, 57, 59, 60, 62, 63, 65, 67, 70, 71, 73, 75, 78, 79, 80, 83, 84, 85, 86, 87, 88, 92, 95, 97, 101, 102, 103, 106, 107, 113, 115, 118, 119
Offset: 1
Taking the first generation of edges to be G(1) = {(3,1)}, the edge (3,1) grows G(2) = {(1,4), (1,5)}, which grows G(3) = {(4,5), (4,9), (5,6), (5,11)}, ... Expelling duplicate nodes and sorting leave (1,2,4,5,6,9,11,...).
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f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 1; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]
Showing 1-3 of 3 results.
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