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A194064 Natural interspersion of A006578; a rectangular array, by antidiagonals. 3
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];

c = Table[c[k], {k, 1, z}]  (* A006578 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

f = Table[f[n], {n, 1, 400}]   (* A194063 *)

r[n_] := Flatten[Position[f, n]]

t[n_, k_] := r[n][[k]]

TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]

p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194064 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]  (* A194065 *)

CROSSREFS

Cf. A194029, A194063, A194065.

Sequence in context: A261830 A194038 A131819 * A194054 A191536 A187076

Adjacent sequences:  A194061 A194062 A194063 * A194065 A194066 A194067

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 14 2011

STATUS

approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)