A194054 -id:A194054 - cp's OEIS frontend

A194058 Inverse permutation to A194054; 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, 36, 11, 17, 24, 25, 26, 34, 35, 44, 45, 16, 23, 31, 32, 33, 42, 43, 53, 54, 55, 66, 22, 30, 39, 40, 41, 51, 52, 63, 64, 65, 77, 78, 29, 38, 48, 49, 50, 61, 62, 74, 75, 76, 89, 90, 91, 105, 37, 47

Offset: 1

Clark Kimberling, Aug 15 2011

nonn

Cf. A194054.

Mathematica
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(See A194054.)
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A194053 Natural fractal sequence of A054347.

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, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8

Offset: 1

Clark Kimberling, Aug 15 2011

nonn

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

Cf. A194029.

z = 40; g = GoldenRatio
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}]  (* A054347 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A194053 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194054 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194058 *)

cp's OEIS Frontend

A194058 Inverse permutation to A194054; every positive integer occurs exactly once.

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