A194062 -id:A194062

Search: a194062 -id:a194062

Displaying 1-2 of 2 results found.

page 1

A194061

Natural interspersion of A002620; a rectangular array, by antidiagonals.

+10
3

1, 2, 3, 4, 5, 8, 6, 7, 11, 15, 9, 10, 14, 19, 24, 12, 13, 18, 23, 29, 35, 16, 17, 22, 28, 34, 41, 48, 20, 21, 27, 33, 40, 47, 55, 63, 25, 26, 32, 39, 46, 54, 62, 71, 80, 30, 31, 38, 45, 53, 61, 70, 79, 89, 99, 36, 37, 44, 52, 60, 69, 78, 88, 98, 109, 120

(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, A194061 is a permutation of the positive integers; its inverse is A194062.

LINKS

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

EXAMPLE

Northwest corner:

1...2...4...6...9...12

3...5...7...10..13..17

8...11..14..18..22..27

15..19..23..28..33..39

24..29..34..40..46..53

MATHEMATICA

z = 50;

c[k_] := Floor[((k + 1)^2)/4];

c = Table[c[k], {k, 1, z}] (* A002620 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

f = Table[f[n], {n, 1, 400}] (* [A122197] *)

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, 11}, {k, 1, n}]] (* A194061 *)

q[n_] := Position[p, n]; Flatten[

Table[q[n], {n, 1, 90}]] (* A194062 *)

CROSSREFS

Cf. A194029, A002620, A122197, A194062.

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 14 2011

STATUS

approved

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 *)