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

Author

Alois P. Heinz, Mar 28 2018

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A007623, A108731, A109381.

Programs

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 *)

Formula

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