A195072 -id:A195072 - cp's OEIS frontend

A195073 Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.

1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 6, 5, 3, 1, 2, 4, 7, 6, 5, 3, 1, 2, 4, 7, 8, 6, 5, 3, 1, 2, 4, 7, 9, 8, 6, 5, 3, 1, 2, 4, 7, 9, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 12, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 13, 12, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[n/sqrt(3)]) is A195072.

Cf. A195072, A194974, A195075.

r = Sqrt[3]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]   (* A195072 *)
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]   (* A195073 *)
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}]]    (* A195074 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A195075 *)

A195074 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 08 2011

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194974 is a permutation of the positive integers, with inverse A195075.

To see that A195074 differs from A194988, note that the generating sequences A195072 and A194986 differ.

			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

Cf. A195072, A195074, A195075.

r = Sqrt[3]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]   (* A195072 *)
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]   (* A195073 *)
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}]]    (* A195074 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A195075 *)

cp's OEIS Frontend

A195073 Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.

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