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%I #5 Mar 30 2012 18:57:44
%S 1,2,3,4,5,6,7,8,10,9,11,12,15,13,14,16,17,21,18,19,20,22,23,28,24,25,
%T 27,26,29,30,36,31,32,35,33,34,37,38,45,39,40,44,41,42,43,46,47,55,48,
%U 49,54,50,51,53,52,56,57,66,58,59,65,60,61,64,62,63,67,68,78
%N Interspersion fractally induced by (1+[2n/3]), where [ ] = floor; a rectangular array, by antidiagonals.
%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194983 is a permutation of the positive integers, with inverse A195096.
%e Northwest corner:
%e 1...2...4...7...11..16
%e 3...5...8...12..17..23
%e 6...10..15..21..28..36
%e 9...13..18..24..31..39
%e 14..19..25..32..40..49
%t r = 2/3; p[n_] := 1 + Floor[n*r]
%t Table[p[n], {n, 1, 90}] (* ess A004396 *)
%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t f[20] (* A195082 *)
%t row[n_] := Position[f[30], n];
%t u = TableForm[Table[row[n], {n, 1, 5}]]
%t v[n_, k_] := Part[row[n], k];
%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, ]
%t {k, 1, n}]] (* A195083 *)
%t q[n_] := Position[w, n]; Flatten[Table[q[n],
%t {n, 1, 80}]] (* A195096 *)
%Y Cf. A004396, A195083, A195096.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 08 2011
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