

A193042


Natural fractal sequence of A194126.


2



1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 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, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..85.


MATHEMATICA

z = 40; g = GoldenRatio;
c[k_] := 1 + Sum[Floor[j + j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}] (* A194126 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 800}] (* A193042 *)
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}]] (* A194100 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194101 *)


CROSSREFS

Cf. A194029, A194126, A194100.
Sequence in context: A283370 A053827 A033926 * A327463 A279478 A050269
Adjacent sequences: A193039 A193040 A193041 * A193043 A193044 A193045


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 15 2011


STATUS

approved



