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A194053 Natural fractal sequence of A054347. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..91.

MATHEMATICA

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 *)

CROSSREFS

Cf. A194029.

Sequence in context: A274459 A225926 A194063 * A194050 A316340 A002828

Adjacent sequences:  A194050 A194051 A194052 * A194054 A194055 A194056

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 15 2011

STATUS

approved

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Last modified October 15 12:24 EDT 2019. Contains 328026 sequences. (Running on oeis4.)