A194060 -id:A194060

The OEIS is supported by the many generous donors to the OEIS Foundation.

Search: a194060 -id:a194060

Displaying 1-1 of 1 result found.

page 1

A194059

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

+10
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

(list; table; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 14 2011

STATUS

approved

page 1

Search completed in 0.006 seconds