

A194051


Natural interspersion of A194050, a rectangular array, by antidiagonals.


3



1, 2, 3, 5, 6, 4, 9, 10, 7, 8, 16, 17, 11, 12, 13, 27, 28, 18, 19, 20, 14, 45, 46, 29, 30, 31, 21, 15, 74, 75, 47, 48, 49, 32, 22, 23, 121, 122, 76, 77, 78, 50, 33, 34, 24, 197, 198, 123, 124, 125, 79, 51, 52, 35, 25, 320, 321, 199, 200, 201, 126, 80, 81, 53
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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, A194051 is a permutation of the positive integers; its inverse is A194052.


LINKS

Table of n, a(n) for n=1..64.


EXAMPLE

Northwest corner:
1...2...5...9...16
3...6...10..17..28
4...7...11..18..29
8...12..19..30..48
13..20..31..49..78


MATHEMATICA

z = 50;
c[k_] := LucasL[k + 1]  2;
c = Table[c[k], {k, 1, z}] (* A014739 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 600}] (* A194050 *)
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, 12}, {k, 1, n}]] (* A194051 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194052 *)


CROSSREFS

Cf. A194029, A014739, A194050, A104052.
Sequence in context: A054077 A194872 A194900 * A195610 A082654 A072636
Adjacent sequences: A194048 A194049 A194050 * A194052 A194053 A194054


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 13 2011


STATUS

approved



