

A194046


Natural interspersion of A052905, a rectangular array, by antidiagonals.


2



1, 5, 2, 10, 6, 3, 16, 11, 7, 4, 23, 17, 12, 8, 9, 31, 24, 18, 13, 14, 15, 40, 32, 25, 19, 20, 21, 22, 50, 41, 33, 26, 27, 28, 29, 30, 61, 51, 42, 34, 35, 36, 37, 38, 39, 73, 62, 52, 43, 44, 45, 46, 47, 48, 49, 86, 74, 63, 53, 54, 55, 56, 57, 58, 59, 60, 100, 87, 75
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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, A194046 is a permutation of the positive integers; its inverse is A194047.


LINKS

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


EXAMPLE

Northwest corner:
1...5...10...16...23
2...6...11...17...24
3...7...12...18...25
4...8...13...19...26
9...14..20...27...35


MATHEMATICA

z = 30;
c[k_] := (k^2 + 5 k  4)/2;
c = Table[c[k], {k, 1, z}] (* A052905 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 255}] (* fractal sequence [A002260] *)
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, 13}, {k, 1, n}]] (* A194046 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194047 *)


CROSSREFS

Cf. A194029, A194047
Sequence in context: A178714 A036121 A162396 * A249368 A055682 A187875
Adjacent sequences: A194043 A194044 A194045 * A194047 A194048 A194049


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 13 2011


STATUS

approved



