A301872 Smallest integer k >= 0 such that the maximum digit of k^2 written in factorial base equals n.

0, 1, 2, 9, 10, 25, 66, 188, 568, 1808, 6024, 20955, 75816, 284520, 1104761, 4428896, 18296575, 77760442, 339474192, 1520281852, 6975531533, 32755301642, 157251442001, 771100761895, 3858854965090, 19692136783074, 102399111271982, 542217184494641

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..806

Formula

a(n) = min { k >= 0 : max(A108731(k^2)) = n } = min { k >= 0 : A109381(k) = n }.

Example

a(11) = 20955: A108731(20955^2) = [11,0,0,0,5,2,4,4,1,1,1].

Mathematica

Block[{nn = 10^5, r, s, t}, t = nn^2; r = Reverse@ Most@ NestWhileList[# + 1 &, 2, #! < t &]; s = Array[Max@ IntegerDigits[#^2, MixedRadix@ r] &, nn, 0]; Map[First@ FirstPosition[s, #] - 1 &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Jan 01 2019 *)

Crossrefs

Cf. A007623, A108731, A109381.

Sequence in context: A079747 A191576 A081346 * A290592 A058551 A119183

Adjacent sequences: A301869 A301870 A301871 * A301873 A301874 A301875

Keyword

nonn,base

Author

Alois P. Heinz, Mar 28 2018

Status

approved