A195184 Interspersion fractally induced by the prime marker sequence A089026.

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).

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

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

Cf. A194959, A089026, A195184, A195185.

Sequence in context: A348356 A209274 A303595 * A194842 A194912 A194866

Adjacent sequences: A195181 A195182 A195183 * A195185 A195186 A195187

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 10 2011

Status

approved