A379298 Largest number k for which k^2 is n digits long and has the maximum sum of digits possible for such a square (A371728(n)).

3, 7, 28, 83, 313, 937, 3114, 9417, 29614, 94863, 298327, 987917, 3162083, 9893887, 29983327, 99483667, 315432874, 994927133, 2999833327, 9486778167, 31464263856, 99497231067, 299998333327, 999949483667, 3160522105583, 9892825177313, 29999983333327

Offset: 1

Author

Zhining Yang, Feb 05 2025

Keywords

• nonn
• base
• more

Examples

			a(6) = 937 because among all 6-digit squares, 698896 = 836^2, 779689 = 883^2, 877969 = 937^2 have the maximum sum of digits 46 = A371728(6), and 937 is the largest.
		

Crossrefs

Cf. A371728, A348303.

Other powers: A380052, A380797, A380566, A380193.

Programs

Mathematica

a[n_] := Module[{s = Floor[Sqrt[(10^n - 1)]], max = 0},
   For[k = s, k >= Ceiling[Sqrt[10^(n - 1)]], k--, t = DigitSum[k^2];
    If[t > max, s = k; max = t]]; s];
Table[a[n], {n, 30}]

Formula

Conjecture: a(2*n) = A348303(n).