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Interspersion fractally induced by the prime marker sequence A089026.
3

%I #11 Nov 06 2017 11:21:45

%S 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 22,28,32,33,34,31,35,30,36,29,41,42,43,40,44,39,45,38,37,51,52,53,50,

%U 54,49,55,48,47,46,61,62,63,60,64,59,65,58,57,56,66,73,74,75

%N Interspersion fractally induced by the prime marker sequence A089026.

%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, 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 G. C. Greubel, <a href="/A195184/b195184.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%e Northwest corner:

%e 1...2...4...8...12..18..24..32

%e 3...5...9...13..19..26..33..42

%e 6...10..14..20..26..34..43..53

%e 7...11..17..23..31..40..50..60

%e 15..21..27..35..44..54..64..76

%t p[n_] := If[PrimeQ[n], n, 1]

%t Table[p[n], {n, 1, 90}] (* A089026 *)

%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] (* A195183 *)

%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}, {k, 1, n}]] (* A195184 *)

%t q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195185 *)

%Y Cf. A194959, A089026, A195184, A195185.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 10 2011