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A194988
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Interspersion fractally induced by A194987, a rectangular array, by antidiagonals.
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6
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1, 3, 2, 6, 4, 5, 10, 7, 9, 8, 15, 11, 14, 12, 13, 21, 16, 20, 17, 19, 18, 28, 22, 27, 23, 26, 25, 24, 36, 29, 35, 30, 34, 33, 31, 32, 45, 37, 44, 38, 43, 42, 39, 41, 40, 55, 46, 54, 47, 53, 52, 48, 51, 49, 50, 66, 56, 65, 57, 64, 63, 58, 62, 59, 61, 60, 78, 67, 77
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OFFSET
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1,2
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COMMENTS
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See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194988 is a permutation of the positive integers, with inverse A194989.
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LINKS
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Table of n, a(n) for n=1..69.
Index entries for sequences that are permutations of the natural numbers
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EXAMPLE
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Northwest corner:
1...3...6...10..15..21
2...4...7...11..16..22
5...9...14..20..27..35
8...12..17..23..30..38
13..19..26..34..43..53
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MATHEMATICA
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r = Sqrt[6]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}] (* A194986 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A194987 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A194988 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194989 *)
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CROSSREFS
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Cf. A194959, A194986, A194988, A194989.
Sequence in context: A059399 A194984 * A195074 A194918 A194915 A195077
Adjacent sequences: A194985 A194986 A194987 * A194989 A194990 A194991
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Sep 07 2011
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STATUS
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approved
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