

A243571


Irregular triangular array generated as in Comments; contains every positive integer exactly once.


8



1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 16, 11, 13, 14, 17, 18, 20, 24, 32, 15, 19, 21, 22, 25, 26, 28, 33, 34, 36, 40, 48, 64, 23, 27, 29, 30, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 65, 66, 68, 72, 80, 96, 128, 31, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 67, 69
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OFFSET

1,2


COMMENTS

Decree that row 1 is (1) and row 2 is (2). For n >=3, row n consists of numbers in increasing order generated as follows: 2*x for each x in row n1 together with 1+2*x for each x in row n2. It is easy to prove that row n consists of F(n) numbers, where F = A000045 (the Fibonacci numbers), and that every positive integer occurs exactly once. Row n has F(n1) even numbers and F(n2) odd numbers.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1500
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

First 6 rows of the array:
1
2
3 ... 4
5 ... 6 ... 8
7 ... 9 ... 10 .. 12 .. 16
11 .. 13 .. 14 .. 17 .. 18 .. 20 .. 24 .. 32
The least and greatest numbers in row n are A083329(n1) and 2^(n1), for n >= 1.


MATHEMATICA

z = 10; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 2 x; h[1] = g[1];
b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n  1]], f2[g[n  1]]]];
h[n_] := h[n] = Union[h[n  1], g[n  1]];
g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]
u = Table[g[n], {n, 1, z}]; v = Flatten[u] (* A243571 *)


CROSSREFS

Cf. A232559, A243572, A243573, A000045.
Sequence in context: A117332 A242704 A334111 * A215366 A333483 A334433
Adjacent sequences: A243568 A243569 A243570 * A243572 A243573 A243574


KEYWORD

nonn,easy,tabf,changed


AUTHOR

Clark Kimberling, Jun 07 2014


STATUS

approved



