A194064 - OEIS

A194064

Natural interspersion of A006578; a rectangular array, by antidiagonals.

1, 4, 2, 8, 5, 3, 14, 9, 6, 7, 21, 15, 10, 11, 12, 30, 22, 16, 17, 18, 13, 40, 31, 23, 24, 25, 19, 20, 52, 41, 32, 33, 34, 26, 27, 28, 65, 53, 42, 43, 44, 35, 36, 37, 29, 80, 66, 54, 55, 56, 45, 46, 47, 38, 39, 96, 81, 67, 68, 69, 57, 58, 59, 48, 49, 50

(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, A194064 is a permutation of the positive integers; its inverse is A194065.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Northwest corner:

1...4...8...14...21...30

2...5...9...15...22...31

3...6...10..16...23...32

7...11..17..24...33...43

12..18..25..34...44...56

MATHEMATICA

z = 50;

c[k_] := k (k + 1)/2 + Floor[(k^2)/4];