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A194067
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Natural interspersion of A087483; a rectangular array, by antidiagonals.
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3
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1, 2, 3, 4, 5, 8, 6, 7, 11, 12, 9, 10, 15, 16, 21, 13, 14, 19, 20, 26, 27, 17, 18, 24, 25, 32, 33, 40, 22, 23, 30, 31, 38, 39, 47, 48, 28, 29, 36, 37, 45, 46, 55, 56, 65, 34, 35, 43, 44, 53, 54, 63, 64, 74, 75, 41, 42, 51, 52, 61, 62, 72, 73, 84, 85, 96, 49, 50, 59
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OFFSET
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1,2
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COMMENTS
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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, A194067 is a permutation of the positive integers; its inverse is A194068.
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LINKS
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EXAMPLE
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Northwest corner:
1...2...4...6...9...13
3...5...7...10..14..18
8...11..15..19..24..30
12..16..20..25..31..37
21..26..32..38..45..53
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MATHEMATICA
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z = 70;
c[k_] := 1 + Floor[(1/3) k^2];
c = Table[c[k], {k, 1, z}] (* A087483 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}] (* A194066 *)
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}]] (* A194067 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194068 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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