

A194059


Natural interspersion of A001911 (Fibonacci numbers minus 2); a rectangular array, by antidiagonals.


2



1, 3, 2, 6, 4, 5, 11, 7, 8, 9, 19, 12, 13, 14, 10, 32, 20, 21, 22, 15, 16, 53, 33, 34, 35, 23, 24, 17, 87, 54, 55, 56, 36, 37, 25, 18, 142, 88, 89, 90, 57, 58, 38, 26, 27, 231, 143, 144, 145, 91, 92, 59, 39, 40, 28, 375, 232, 233, 234, 146, 147, 93, 60, 61, 41, 29
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OFFSET

1,2


COMMENTS

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194059 is a permutation of the positive integers; its inverse is A194060.


LINKS

Table of n, a(n) for n=1..66.


EXAMPLE

Northwest corner:
1...3...6...11...19
2...4...7...12...30
5...8...13..21...34
9...14..22..35...56
10..15..23..36...57


MATHEMATICA

z = 50;
c[k_] := 2 + Fibonacci[k + 3];
c = Table[c[k], {k, 1, z}] (* A001911, F(n+3)2 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 700}] (* cf. A194055 *)
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, 12}, {k, 1, n}]] (* A194059 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 100}]] (* A194060 *)


CROSSREFS

Cf. A194029, A194059, A194062.
Sequence in context: A064789 A195111 A274315 * A191427 A191428 A191733
Adjacent sequences: A194056 A194057 A194058 * A194060 A194061 A194062


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 14 2011


STATUS

approved



