This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(6) = 46 because 46 is the largest digital sum encountered among all 6-digit squares (698896, 779689, 877969).
Array[Max@Map[Total@IntegerDigits[#^2] &, Range[Floor@Sqrt[10^(#)]], Floor@Sqrt[10^(# + 1) - 1]] &, 15]
F:= proc(d)
local s, P, nP, S, x, bestx;
bestx:= 0;
for s in [1,3,6,9] do
for P in map(op @combinat:-permute, combinat:-partition(s)) do
nP:= nops(P);
for S in map(t -> [d-1, op(t)], combinat:-choose([$0..d-2],nP-1)) do
x:= add(P[i]*10^S[i],i=1..nP);
if x > bestx and issqr(1+8*x) then bestx:= x fi;
od;
od;
if bestx > 0 then return bestx fi;
od;
end proc:
seq(F(d),d=1..30); # Robert Israel, May 25 2016
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