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%I #11 May 21 2016 22:43:09
%S 4,97344,462400,473344,506944,846400,78854400,444622240000,
%T 448417729600,454125036544,551027105344,824681934400,983984641600,
%U 460651783840000,6703941381760000,444446222224000000,459134832243732544,462218702574222400,462583182938702400
%N Squares that remain squares if you decrease them by 4 times a repunit with the same number of digits.
%C Every term ends in 0 or 4.
%H Giovanni Resta, <a href="/A273231/b273231.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 - 4*1 = 0 = 0^2;
%e 97344 - 4*11111 = 52900 = 230^2;
%e 462400 - 4*111111 = 17956 = 134^2.
%p P:=proc(q,h) local n; for n from 1 to q do
%p if type(sqrt(n^2-h*(10^(ilog10(n^2)+1)-1)/9),integer) then print(n^2);
%p fi; od; end: P(10^9,4);
%t sol[k_] := Block[{x, e = IntegerLength@k, d = Divisors@ k}, Union[ #+k/# & /@ Select[ Take[d, Ceiling[ Length@d/2]], EvenQ[x = #+k/#] && IntegerLength[ x^2/4] == e &]]^2/4]; r[n_] := 4 (10^n-1)/9; Flatten[sol /@ r /@ Range[12]] (* _Giovanni Resta_, May 18 2016 *)
%Y Cf. A002275, A061844, A273299, A273230, A273232-A273234.
%K nonn,easy,base
%O 1,1
%A _Paolo P. Lava_, May 18 2016
%E a(16)-a(19) from _Giovanni Resta_, May 18 2016
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