The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let S be the set of numbers defined by these rules: 1 is in S, and if x is in S, then x + 1 and 2*x + 3 are in S. Then S is the set of positive integers, which arise in generations. Deleting duplicates as they occur, the generations are given by g(1) = (1), g(2) = (2,5), g(3) = (3,7,6,13), etc. Concatenating these gives A232644, a permutation of the positive integers. For n > 2, the number of numbers in g(n) is L(n), where F = A000032, the Lucas numbers. It is helpful to show the results as a tree with the terms of S as nodes, an edge from x to x + 1 if x + 1 has not already occurred, and an edge from x to 2*x + 3 if 2*x + 3 has not already occurred. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE 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). 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 *) CROSSREFS Cf. A000032, A232559, A232639, A232645. Sequence in context: A328827 A181184 A078383 * A125512 A272908 A191432 Adjacent sequences: A232641 A232642 A232643 * A232645 A232646 A232647 KEYWORD nonn,easy AUTHOR Clark Kimberling, Nov 28 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 9 06:26 EDT 2024. Contains 375759 sequences. (Running on oeis4.)