

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
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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



