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A195184 Interspersion fractally induced by the prime marker sequence A089026.

%I A195184 #11 Nov 06 2017 11:21:45
%S A195184 1,2,3,4,5,6,8,9,10,7,12,13,14,11,15,18,19,20,17,21,16,24,25,26,23,27,
%T A195184 22,28,32,33,34,31,35,30,36,29,41,42,43,40,44,39,45,38,37,51,52,53,50,
%U A195184 54,49,55,48,47,46,61,62,63,60,64,59,65,58,57,56,66,73,74,75
%N A195184 Interspersion fractally induced by the prime marker sequence A089026.
%C A195184 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194184 is a permutation of the positive integers, with inverse A195185. (The prime marker sequence A089026 is given by p(n)=n if n is prime and p(n)=1 otherwise).
%H A195184 G. C. Greubel, <a href="/A195184/b195184.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e A195184 Northwest corner:
%e A195184 1...2...4...8...12..18..24..32
%e A195184 3...5...9...13..19..26..33..42
%e A195184 6...10..14..20..26..34..43..53
%e A195184 7...11..17..23..31..40..50..60
%e A195184 15..21..27..35..44..54..64..76
%t A195184 p[n_] := If[PrimeQ[n], n, 1]
%t A195184 Table[p[n], {n, 1, 90}]  (* A089026 *)
%t A195184 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195184 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195184 f[20] (* A195183 *)
%t A195184 row[n_] := Position[f[30], n];
%t A195184 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195184 v[n_, k_] := Part[row[n], k];
%t A195184 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A195184 *)
%t A195184 q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A195185 *)
%Y A195184 Cf. A194959, A089026, A195184, A195185.
%K A195184 nonn,tabl
%O A195184 1,2
%A A195184 _Clark Kimberling_, Sep 10 2011