A194922 -id:A194922 - cp's OEIS frontend

A195071 Inverse permutation of A194922; every positive integer occurs exactly once.

1, 3, 2, 6, 5, 4, 9, 10, 8, 7, 13, 15, 14, 12, 11, 18, 21, 20, 19, 17, 16, 24, 27, 28, 26, 25, 23, 22, 31, 34, 36, 35, 33, 32, 30, 29, 39, 42, 45, 44, 43, 41, 40, 38, 37, 48, 51, 55, 54, 53, 52, 50, 49, 47, 46, 58, 61, 65, 66, 64, 63, 62, 60, 59, 57, 56, 69, 72, 76

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A194922, A194921, A194920, A194959.

r = Sqrt[2]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194920 *)
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]  (* A194921 *)
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}]]  (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A195071 *)

A194920 a(n) = n - floor(n/sqrt(2)).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23

Offset: 1

Clark Kimberling, Sep 08 2011

a(n) is the number of zeros in row n+1 in triangle A255195. - Mats Granvik, Feb 18 2015.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A194921.

[n-Floor(n/Sqrt(2)): n in [1..80] ]; // Vincenzo Librandi, Sep 10 2011

r = Sqrt[2]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194920 *)
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]  (* A194921 *)
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}]]  (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A195071 *)

vector(100,n,n-floor(n/sqrt(2))) \\ Derek Orr, Feb 28 2015

A194921 Fractalization of (n - [n/sqrt(2)]), where [ ]=floor.

Original entry on oeis.org

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

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(2)]) is A194920.

G. C. Greubel, Table of n, a(n) for n = 1..5050

Cf. A194920, A194922, A195071.

r = Sqrt[2]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194920 *)
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]  (* A194921 *)
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}]]  (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A195071 *)

cp's OEIS Frontend

A195071 Inverse permutation of A194922; every positive integer occurs exactly once.

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A194920 a(n) = n - floor(n/sqrt(2)).

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A194921 Fractalization of (n - [n/sqrt(2)]), where [ ]=floor.

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