

A274455


Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x 1 and 2*x are in S, and duplicates are deleted as they occur.


1



1, 0, 2, 1, 4, 2, 3, 8, 3, 4, 6, 7, 16, 6, 5, 8, 5, 12, 14, 15, 32, 7, 12, 10, 9, 16, 10, 11, 24, 13, 28, 30, 31, 64, 14, 13, 24, 11, 20, 18, 17, 32, 9, 20, 22, 23, 48, 26, 27, 56, 29, 60, 62, 63, 128, 15, 28, 26, 25, 48, 22, 21
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OFFSET

1,3


COMMENTS

Every integer occurs exactly once. The rules for this tree become identical to those for A232559 when "x + 1" is substituted for "x  1".
For n > 3, the nth generation has F(n) nodes, of which F(n1) are positive and F(n2) are negative, where F = A000045, the Fibonacci numbers.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10946


EXAMPLE

Generation g(1) consists of the seed, 1; generation g(2) consists of 0 and 2 from which 0 begets 1 and 0, but this 0 is a duplicate and is removed, while 2 begets 1 and 4, with 1 removed, so that g(3) = {1,4}. Thereafter, g(4) = {2,3,8}, g(5) = {3,4,6,7,16}, etc.


MATHEMATICA

z = 12; g[1] = {1}; g[2] = {0, 2};
g[n_] := Riffle[g[n  1]  1, 2 g[n  1]];
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}]] (*A274455*)


CROSSREFS

Cf. A000045, A232559.
Sequence in context: A121464 A090278 A256143 * A153279 A278425 A309019
Adjacent sequences: A274452 A274453 A274454 * A274456 A274457 A274458


KEYWORD

sign,easy


AUTHOR

Clark Kimberling, Jun 23 2016


STATUS

approved



