A194071 -id:A194071 - cp's OEIS frontend

A194072 Inverse permutation to A194071; every positive integer occurs exactly once.

1, 3, 2, 5, 6, 10, 4, 8, 9, 14, 7, 12, 13, 19, 15, 21, 11, 17, 18, 25, 20, 27, 28, 36, 16, 23, 24, 32, 26, 34, 35, 44, 22, 30, 31, 40, 33, 42, 43, 53, 45, 55, 29, 38, 39, 49, 41, 51, 52, 63, 54, 65, 66, 78, 37, 47, 48, 59, 50, 61, 62, 74, 64, 76, 77, 90, 46, 57, 58

Offset: 1

Clark Kimberling, Aug 14 2011

nonn

Cf. A194071.

Mathematica
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(See A194071.)
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A194070 Natural fractal sequence of A194069.

Original entry on oeis.org

1, 2, 1, 2, 3, 4, 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, 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, 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

Offset: 1

Clark Kimberling, Aug 14 2011

nonn

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

Cf. A194029, A194069, A194071.

z = 70;
c[k_] := 1 + Floor[(2/3) k^2];
c = Table[c[k], {k, 1, z}]  (* A194069 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194070 *)
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, 14}, {k, 1, n}]] (* A194071 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194072 *)

A194069 1+floor((2/3)*n^2).

Original entry on oeis.org

1, 3, 7, 11, 17, 25, 33, 43, 55, 67, 81, 97, 113, 131, 151, 171, 193, 217, 241, 267, 295, 323, 353, 385, 417, 451, 487, 523, 561, 601, 641, 683, 727, 771, 817, 865, 913, 963, 1015, 1067, 1121, 1177, 1233, 1291, 1351, 1411

Offset: 1

Clark Kimberling, Aug 14 2011

nonn

Cf. A194070 (natural fractal sequence),

A194071 (natural fractal interspersion).

c[k_]:=1+Floor[(2/3)k^2]; c=Table[c[k],{k,1,90}]

a(n)=1+floor(2*n^2/3).

a(n) = 1 +A030511(n+1). - R. J. Mathar, Aug 25 2011

cp's OEIS Frontend

A194072 Inverse permutation to A194071; every positive integer occurs exactly once.

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A194070 Natural fractal sequence of A194069.

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A194069 1+floor((2/3)*n^2).

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