A232644 Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x + 1 and 2*x + 3 are in S, and duplicates are deleted as they occur.
1, 2, 5, 3, 7, 6, 13, 4, 9, 8, 17, 15, 14, 29, 11, 10, 21, 19, 18, 37, 16, 33, 31, 30, 61, 12, 25, 23, 22, 45, 20, 41, 39, 38, 77, 35, 34, 69, 32, 65, 63, 62, 125, 27, 26, 53, 24, 49, 47, 46, 93, 43, 42, 85, 40, 81, 79, 78, 157, 36, 73, 71, 70, 141, 67, 66
Offset: 1
Examples
Each x begets x + 1 and 2*x + 3, but if either has already occurred it is deleted. Thus, 1 begets 2 and 5; then 2 begets 3 and 7, and 5 begets 6 and 13, so that g(3) = (3,7,6,13).
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
z = 14; g[1] = {1}; g[2] = {2}; g[n_] := Riffle[g[n - 1] + 1, 2 g[n - 1] + 3]; j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]]; g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]]; g1[1] = g[1]; g1[2] = g[2]; t = Flatten[Table[g1[n], {n, 1, z}]] (* A232644 *) Table[Length[g1[n]], {n, 1, z}] (* A000032 *) Flatten[Table[Position[t, n], {n, 1, 200}]] (* A232645 *)
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