A049416
Largest number whose square has n digits.
Original entry on oeis.org
3, 9, 31, 99, 316, 999, 3162, 9999, 31622, 99999, 316227, 999999, 3162277, 9999999, 31622776, 99999999, 316227766, 999999999, 3162277660, 9999999999, 31622776601, 99999999999, 316227766016, 999999999999, 3162277660168
Offset: 1
Ulrich Schimke (ulrschimke(AT)aol.com)
31^2 = 961, but 32^2 = 1024, hence a(3) = 31.
a(4) = 99: 99^2 = 9801 has 4 digits, while 100^2 = 10000 has 5 digits.
More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001
A180416
Number of positive integers below 10^n, excluding perfect squares, which have a representation as a sum of 2 positive squares.
Original entry on oeis.org
3, 33, 298, 2649, 23711, 215341, 1982296, 18447847, 173197435, 1637524156, 15570196516, 148735628858, 1426303768587, 13722207893214, 132387231596281, 1280309591127436
Offset: 1
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isA000415 := proc(n) local x ,y2; if issqr(n) then false; else for x from 1 do y2 := n-x^2 ; if y2 < x^2 then return false; elif issqr(y2) then return true; end if; end do ; end if; end proc:
A180416 := proc(n) a := 0 ; for k from 2 to 10^n-1 do if isA000415(k) then a := a+1 ; end if; end do: a ; end proc:
for n from 1 do print(A180416(n)) ; end do; # R. J. Mathar, Jan 20 2011
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a[n_] := a[n] = Module[{k, xMax = Floor[Sqrt[10^n - 1]]}, Table[k = x^2 + y^2; If[IntegerQ[Sqrt[k]], Nothing, k], {x, 1, xMax}, {y, x, Floor[ Sqrt[10^n - 1 - x^2]]}] // Flatten // Union // Length];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 8}] (* Jean-François Alcover, Oct 31 2020 *)
A180425
Number of positive integers below 10^n requiring 3 positive squares in their representation as sum of squares.
Original entry on oeis.org
2, 42, 505, 5586, 59308, 616995, 6347878, 64875490, 660104281, 6695709182, 67762820595, 684596704482, 6907026402474, 69611115440126, 700946070114283, 7053023642205904
Offset: 1
A180347
The number of n-digit numbers requiring 4 nonzero squares in their representation as sum of squares.
Original entry on oeis.org
1, 14, 150, 1500, 14999, 150000, 1499999, 15000000, 149999998, 1500000001, 14999999999, 149999999999, 1500000000001, 14999999999999, 149999999999999, 1500000000000001, 14999999999999998, 149999999999999999, 1500000000000000003, 14999999999999999996
Offset: 1
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