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, 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

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 n-th generation has F(n) nodes, of which F(n-1) are positive and F(n-2) 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: A090278 A256143 A352791 * A153279 A278425 A309019

Adjacent sequences: A274452 A274453 A274454 * A274456 A274457 A274458

Keyword

sign,easy

Author

Clark Kimberling, Jun 23 2016

Status

approved