

A194011


Natural interspersion of A002061; a rectangular array, by antidiagonals.


3



1, 3, 2, 7, 4, 5, 13, 8, 9, 6, 21, 14, 15, 10, 11, 31, 22, 23, 16, 17, 12, 43, 32, 33, 24, 25, 18, 19, 57, 44, 45, 34, 35, 26, 27, 20, 73, 58, 59, 46, 47, 36, 37, 28, 29, 91, 74, 75, 60, 61, 48, 49, 38, 39, 30, 111, 92, 93, 76, 77, 62, 63, 50, 51, 40, 41, 133, 112
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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, A194011 is a permutation of the positive integers; its inverse is A194012.


LINKS

Table of n, a(n) for n=1..68.


EXAMPLE

Northwest corner:
1...3...7...13...21...31
2...4...8...14...22...32
5...9...15..23...33...45
6...10..16..24...34...46
11..17..25..35...47...61


MATHEMATICA

z = 40;
c[k_] := k^2  k + 1
c = Table[c[k], {k, 1, z}] (* A002061 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 800}] (* A074294 *)
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, 16}, {k, 1, n}]] (* A194011 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194012 *)


CROSSREFS

Cf. A194029, A002061, A074294, A194012.
Sequence in context: A194104 A277679 A108644 * A303763 A303765 A255555
Adjacent sequences: A194008 A194009 A194010 * A194012 A194013 A194014


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 15 2011


STATUS

approved



