A194064 -id:A194064 - cp's OEIS frontend

A194065 Inverse permutation to A194064; every positive integer occurs exactly once.

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

Offset: 1

Clark Kimberling, Aug 14 2011

nonn

Cf. A194064.

Mathematica
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(See A194064.)
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A194063 Natural fractal sequence of A006578.

Original entry on oeis.org

1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Offset: 1

Clark Kimberling, Aug 14 2011

nonn

See A194029 for definitions of natural fractal sequence and natural interspersion.

Cf. A194029, A006578, A194064, A194065.

z = 50;
c[k_] := k (k + 1)/2 + Floor[(k^2)/4];
c = Table[c[k], {k, 1, z}]  (* A006578 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 400}]   (* A194063 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194064 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]  (* A194065 *)

cp's OEIS Frontend

A194065 Inverse permutation to A194064; every positive integer occurs exactly once.

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