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A194032 Natural interspersion of the squares (1,4,9,16,25,...), a rectangular array, by antidiagonals. 3
1, 4, 2, 9, 5, 3, 16, 10, 6, 7, 25, 17, 11, 12, 8, 36, 26, 18, 19, 13, 14, 49, 37, 27, 28, 20, 21, 15, 64, 50, 38, 39, 29, 30, 22, 23, 81, 65, 51, 52, 40, 41, 31, 32, 24, 100, 82, 66, 67, 53, 54, 42, 43, 33, 34, 121, 101, 83, 84, 68, 69, 55, 56, 44, 45 (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, A194032 is a permutation of the positive integers; its inverse is A194033.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

Northwest corner:

1...4...9...16...25

2...5...10..17...26

3...6...11..18...27

7...12..19..28...39

8...13..20..29...40

MATHEMATICA

z = 30;

c[k_] := k^2;

c = Table[c[k], {k, 1, z}]  (* A000290 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] (* A071797 *)

f = Table[f[n], {n, 1, 255}]

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, 14}, {k, 1, n}]] (* A194032 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194033 *)

CROSSREFS

Cf. A000290, A071797, A194033, A192872.

Sequence in context: A157647 A194108 A091452 * A191739 A091450 A163253

Adjacent sequences:  A194029 A194030 A194031 * A194033 A194034 A194035

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 12 2011

STATUS

approved

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Last modified October 1 12:58 EDT 2020. Contains 337443 sequences. (Running on oeis4.)