A195183 -id:A195183 - cp's OEIS frontend

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

Clark Kimberling, Sep 10 2011

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).

			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

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

Cf. A194959, A089026, A195184, A195185.

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 *)

A195185 Inverse permutation of A195184; every positive integer occurs exactly once.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 10, 7, 8, 9, 14, 11, 12, 13, 15, 21, 19, 16, 17, 18, 20, 27, 25, 22, 23, 24, 26, 28, 36, 34, 32, 29, 30, 31, 33, 35, 45, 44, 42, 40, 37, 38, 39, 41, 43, 55, 54, 53, 51, 49, 46, 47, 48, 50, 52, 65, 64, 63, 61, 59, 56, 57, 58, 60, 62, 66, 78, 76, 75

Offset: 1

Clark Kimberling, Sep 10 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A195183, A195184, A089026, A194959.

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 *)

cp's OEIS Frontend

A195184 Interspersion fractally induced by the prime marker sequence A089026.

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