

A194064


Natural interspersion of A006578; a rectangular array, by antidiagonals.


3



1, 4, 2, 8, 5, 3, 14, 9, 6, 7, 21, 15, 10, 11, 12, 30, 22, 16, 17, 18, 13, 40, 31, 23, 24, 25, 19, 20, 52, 41, 32, 33, 34, 26, 27, 28, 65, 53, 42, 43, 44, 35, 36, 37, 29, 80, 66, 54, 55, 56, 45, 46, 47, 38, 39, 96, 81, 67, 68, 69, 57, 58, 59, 48, 49, 50
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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, A194064 is a permutation of the positive integers; its inverse is A194065.


LINKS

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


EXAMPLE

Northwest corner:
1...4...8...14...21...30
2...5...9...15...22...31
3...6...10..16...23...32
7...11..17..24...33...43
12..18..25..34...44...56


MATHEMATICA

z = 50;
c[k_] := k (k + 1)/2 + Floor[(k^2)/4];
c = Table[c[k], {k, 1, z}] (* A006578 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 400}] (* A194063 *)
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}]] (* A194064 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194065 *)


CROSSREFS

Cf. A194029, A194063, A194065.
Sequence in context: A261830 A194038 A131819 * A194054 A191536 A187076
Adjacent sequences: A194061 A194062 A194063 * A194065 A194066 A194067


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 14 2011


STATUS

approved



