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%I #6 Mar 30 2012 18:57:39
%S 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,
%T 21,22,50,41,33,26,27,28,29,30,61,51,42,34,35,36,37,38,39,73,62,52,43,
%U 44,45,46,47,48,49,86,74,63,53,54,55,56,57,58,59,60,100,87,75
%N Natural interspersion of A052905, a rectangular array, by antidiagonals.
%C 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.
%e Northwest corner:
%e 1...5...10...16...23
%e 2...6...11...17...24
%e 3...7...12...18...25
%e 4...8...13...19...26
%e 9...14..20...27...35
%t z = 30;
%t c[k_] := (k^2 + 5 k - 4)/2;
%t c = Table[c[k], {k, 1, z}] (* A052905 *)
%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t f = Table[f[n], {n, 1, 255}] (* fractal sequence [A002260] *)
%t r[n_] := Flatten[Position[f, n]]
%t t[n_, k_] := r[n][[k]]
%t TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A194046 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194047 *)
%Y Cf. A194029, A194047
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 13 2011
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