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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
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
Sequence in context: A157647 A194108 A091452 * A191739 A091450 A163253
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 12 2011
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)