A194054 - OEIS

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A194054

Natural interspersion of A054347; a rectangular array, by antidiagonals.

1, 4, 2, 8, 5, 3, 14, 9, 6, 7, 22, 15, 10, 11, 12, 31, 23, 16, 17, 18, 13, 42, 32, 24, 25, 26, 19, 20, 54, 43, 33, 34, 35, 27, 28, 21, 68, 55, 44, 45, 46, 36, 37, 29, 30, 84, 69, 56, 57, 58, 47, 48, 38, 39, 40, 101, 85, 70, 71, 72, 59, 60, 49, 50, 51, 41, 120, 102

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194054 is a permutation of the positive integers; its inverse is A194055.

LINKS

Table of n, a(n) for n=1..68.

EXAMPLE

Northwest corner:

1...4...8...14...22...31

2...5...9...15...23...32

3...6...10..16...24...33

7...11..17..25...34...45

MATHEMATICA

z = 40; g = GoldenRatio

c[k_] := Sum[Floor[j*g], {j, 1, k}];

c = Table[c[k], {k, 1, z}] (* A054347 *)