A054077 Inverse of the permutation A054073 of N.

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

Offset

1,2

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.)

Links

Table of n, a(n) for n=1..63.

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

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 *)

Crossrefs

Sequence in context: A194863 A194833 A195108 * A194872 A194900 A194051

Adjacent sequences: A054074 A054075 A054076 * A054078 A054079 A054080

Keyword

nonn

Author

Clark Kimberling

Status

approved