A195081 -id:A195081 - cp's OEIS frontend

A195079 Fractalization of (1+[n/4]), where [ ]=floor.

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

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 (1+[n/4]) is A008621. See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

Cf. A008621, A195080, A195081.

r = 4; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A008621 *)
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] (* A195079 *)
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}]] (* A195080 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195081 *)

A195080 Interspersion fractally induced by A008621, a rectangular array, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 5, 4, 10, 9, 7, 8, 15, 14, 11, 13, 12, 21, 20, 16, 19, 18, 17, 28, 27, 22, 26, 25, 24, 23, 36, 35, 29, 34, 33, 32, 30, 31, 45, 44, 37, 43, 42, 41, 38, 40, 39, 55, 54, 46, 53, 52, 51, 47, 50, 49, 48, 66, 65, 56, 64, 63, 62, 57, 61, 60, 59, 58, 78, 77, 67

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, A194980 is a permutation of the positive integers, with inverse A195081.

			Northwest corner:
1...3...6...10..15..21..38
2...5...9...14..20..27..35
4...7...11..16..22..29..37
8...13..19..26..34..43..53
12..18..25..33..42..52..63

Cf. A008621, A195079, A195081.

r = 4; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A008621 *)
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] (* A195079 *)
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}]] (* A195080 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195081 *)

cp's OEIS Frontend

A195079 Fractalization of (1+[n/4]), where [ ]=floor.

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