A182857 Smallest number that requires exactly n iterations to reach a fixed point under the x -> A181819(x) map.

1, 3, 4, 6, 12, 60, 2520, 1286485200, 35933692027611398678865941374040400000

Offset

0,2

Comments

a(9) has 296 digits.

Related to Levine's sequence (A011784): A011784(n) = A001222(a(n)) = A001221(a(n+1)) = A051903(a(n+2)) = A071625(a(n+2)). Also see A182858.

Values of n where A182850(n) increases to a record.

The multiplicity of prime(k) in a(n+1) is the k-th largest prime index of a(n), which is A296150(a(n),k). - Gus Wiseman, May 13 2018

Links

Gus Wiseman, Table of n, a(n) for n = 0..9

Formula

For n > 0, a(n) = A181819(a(n+1)). For n > 1, a(n) = A181821(a(n-1)).

Example

From Gus Wiseman, May 13 2018: (Start)
Like A001462 the following sequence of multisets whose Heinz numbers belong to this sequence is a run-length describing sequence, as the number of k's in row n + 1 is equal to the k-th term of row n.
{2}
{1,1}
{1,2}
{1,1,2}
{1,1,2,3}
{1,1,1,2,2,3,4}
{1,1,1,1,2,2,2,3,3,4,4,5,6,7}
{1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8,8,9,9,10,10,11,12,13,14}
(End)

Mathematica

Prepend[Function[m, Times@@Prime/@m]/@NestList[Join@@Table[Table[i, {Reverse[#][[i]]}], {i, Length[#]}]&, {2}, 8], 1] (* Gus Wiseman, May 13 2018 *)

Crossrefs

Cf. A001462, A007755, A007916, A009287, A012257, A112798, A181819, A182850-A182858, A296150, A304455, A304464, A304465.

Sequence in context: A137333 A006719 A202855 * A251483 A009287 A061080

Adjacent sequences: A182854 A182855 A182856 * A182858 A182859 A182860

Keyword

nonn

Author

Matthew Vandermast, Jan 05 2011

Status

approved