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

1,1

Links

Table of n, a(n) for n=1..27.

Formula

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

Example

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.

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}]

Crossrefs

Cf. A371728, A348303.

Other powers: A380052, A380797, A380566, A380193.

Sequence in context: A351771 A148757 A148758 * A054277 A393000 A197960

Adjacent sequences: A379295 A379296 A379297 * A379299 A379300 A379301

Keyword

nonn,base,more

Author

Zhining Yang, Feb 05 2025

Status

approved