

A194030


Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), a rectangular array, by antidiagonals.


3



1, 2, 4, 3, 6, 7, 5, 9, 10, 11, 8, 14, 15, 16, 12, 13, 22, 23, 24, 17, 18, 21, 35, 36, 37, 25, 26, 19, 34, 56, 57, 58, 38, 39, 27, 20, 55, 90, 91, 92, 59, 60, 40, 28, 29, 89, 145, 146, 147, 93, 94, 61, 41, 42, 30, 144, 234, 235, 236, 148, 149, 95, 62, 63, 43, 31
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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, A194030 is a permutation of the positive integers; its inverse is A194031.


LINKS

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


EXAMPLE

Northwest corner:
1...2...3...5...8...13
4...6...9...14..22..35
7...10..15..23..36..57
11..16..24..37..58..92
12..17..25..38..59..93


MATHEMATICA

z = 40;
c[k_] := Fibonacci[k + 1];
c = Table[c[k], {k, 1, z}] (* A000045 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 800}] (* A194029 *)
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, 13}, {k, 1, n}]] (* A194030 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194031 *)


CROSSREFS

Cf. A194029, A194031.
Sequence in context: A297551 A297673 A083050 * A083044 A126714 A035506
Adjacent sequences: A194027 A194028 A194029 * A194031 A194032 A194033


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 12 2011


STATUS

approved



