

A243573


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


4



1, 2, 4, 3, 5, 8, 16, 6, 9, 12, 17, 20, 32, 64, 7, 10, 13, 18, 21, 24, 33, 36, 48, 65, 68, 80, 128, 256, 11, 14, 19, 22, 25, 28, 34, 37, 40, 49, 52, 66, 69, 72, 81, 84, 96, 129, 132, 144, 192, 257, 260, 272, 320, 512, 1024, 15, 23, 26, 29, 35, 38, 41, 44, 50
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OFFSET

1,2


COMMENTS

Decree that (row 1) = (1), (row 2) = (2, 4), (row 3) = (3,5,8,16), (row 4) = (6,9,12,17,20,32,64). Let r(n) = A001563(n+3), so that r(r) = r(n1) + r(n2) + r(n3) + r(n4) with r(1) =1, r(2) = 2, r(3) = 4, r(4) = 7. Row n of the array, for n >= 5, consists of the numbers, in increasing order, defined as follows: all 4*x from x in row n1, together with all 1 + 4*x from x in row n2, together with all 2 + 4*x from x in row n3, together with all 3 + 4*x for x in row n4. Thus, the number of numbers in row n is r(n), a tetranacci number. Every positive integer occurs exactly once in the array, so that the resulting sequence is a permutation of the positive integers.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..2500


EXAMPLE

First 5 rows of the array:
1
2 .. 4
3 .. 5 .. 8 .. 16
6 .. 9 .. 12 . 17 . 20 . 32 . 64
7 .. 10 . 13 . 18 . 21 . 24 . 33 . 36 . 48 . 65 . 68 . 80 . 128 . 256


MATHEMATICA

z = 8; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4 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] (* A243573 *)


CROSSREFS

Cf. A243571, A243572, A001631, A232563.
Sequence in context: A249683 A215898 A246162 * A132193 A185910 A306779
Adjacent sequences: A243570 A243571 A243572 * A243574 A243575 A243576


KEYWORD

nonn,easy,tabf


AUTHOR

Clark Kimberling, Jun 07 2014


STATUS

approved



