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A195184
Interspersion fractally induced by the prime marker sequence A089026.
3
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, 22, 28, 32, 33, 34, 31, 35, 30, 36, 29, 41, 42, 43, 40, 44, 39, 45, 38, 37, 51, 52, 53, 50, 54, 49, 55, 48, 47, 46, 61, 62, 63, 60, 64, 59, 65, 58, 57, 56, 66, 73, 74, 75
OFFSET
1,2
COMMENTS
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).
EXAMPLE
Northwest corner:
1...2...4...8...12..18..24..32
3...5...9...13..19..26..33..42
6...10..14..20..26..34..43..53
7...11..17..23..31..40..50..60
15..21..27..35..44..54..64..76
MATHEMATICA
p[n_] := If[PrimeQ[n], n, 1]
Table[p[n], {n, 1, 90}] (* A089026 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A195183 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A195184 *)
q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195185 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 10 2011
STATUS
approved