

A194071


Natural interspersion of A194069; a rectangular array, by antidiagonals.


4



1, 3, 2, 7, 4, 5, 11, 8, 9, 6, 17, 12, 13, 10, 15, 25, 18, 19, 14, 21, 16, 33, 26, 27, 20, 29, 22, 23, 43, 34, 35, 28, 37, 30, 31, 24, 55, 44, 45, 36, 47, 38, 39, 32, 41, 67, 56, 57, 46, 59, 48, 49, 40, 51, 42, 81, 68, 69, 58, 71, 60, 61, 50, 63, 52, 53, 97, 82, 83
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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, A194071 is a permutation of the positive integers; its inverse is A194072.


LINKS

Table of n, a(n) for n=1..69.


EXAMPLE

Northwest corner:
1...3...7...11...17
2...4...8...12...18
5...9...13..19...27
6...10..14..20...28
15..21..29..37...47


MATHEMATICA

z = 70;
c[k_] := 1 + Floor[(2/3) k^2];
c = Table[c[k], {k, 1, z}] (* A194069 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 300}] (* A194070 *)
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, 14}, {k, 1, n}]] (* A194071 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194072 *)


CROSSREFS

Cf. A194029, A194069, A194070, A194072.
Sequence in context: A175057 A153154 A154438 * A194104 A277679 A108644
Adjacent sequences: A194068 A194069 A194070 * A194072 A194073 A194074


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 14 2011


STATUS

approved



