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A054077
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Inverse of the permutation A054073 of N.
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3
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1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 13, 15, 12, 14, 11, 18, 21, 17, 20, 16, 19, 24, 27, 23, 26, 22, 25, 28, 32, 35, 30, 34, 29, 33, 36, 31, 40, 44, 38, 42, 37, 41, 45, 39, 43, 50, 54, 48, 52, 46, 51, 55, 49, 53, 47, 60, 65, 58, 63, 56, 61, 66, 59
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| When formatted as a rectangular array, row n gives the positions of n in A054073; the array is an interspersion. (Each pair of rows eventually intersperse.)
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EXAMPLE
| Northwest corner when formatted as an interspersion:
1...2...5...8...13..18
3...6...10..15..21..27
4...7...12..17..23..30
9...14..20..26..34..42
11..16..22..29..37..46
19..25..33..41..51..61
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MATHEMATICA
| r = Sqrt[2];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]],
{n, 1, 20}]] (* A054073 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A054077 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]] (* A054076 *)
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CROSSREFS
| Sequence in context: A194863 A194833 A195108 * A194872 A194900 A194051
Adjacent sequences: A054074 A054075 A054076 * A054078 A054079 A054080
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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