A273231 Squares that remain squares if you decrease them by 4 times a repunit with the same number of digits.

4, 97344, 462400, 473344, 506944, 846400, 78854400, 444622240000, 448417729600, 454125036544, 551027105344, 824681934400, 983984641600, 460651783840000, 6703941381760000, 444446222224000000, 459134832243732544, 462218702574222400, 462583182938702400

Offset

1,1

Comments

Every term ends in 0 or 4.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

4 - 4*1 = 0 = 0^2;
97344 - 4*11111 = 52900 = 230^2;
462400 - 4*111111 = 17956 = 134^2.

Maple

P:=proc(q, h) local n; for n from 1 to q do
if type(sqrt(n^2-h*(10^(ilog10(n^2)+1)-1)/9), integer) then print(n^2);
fi; od; end: P(10^9, 4);

Mathematica

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 *)

Crossrefs

Cf. A002275, A061844, A273299, A273230, A273232-A273234.

Sequence in context: A066544 A009529 A339450 * A360760 A239021 A193151

Adjacent sequences: A273228 A273229 A273230 * A273232 A273233 A273234

Keyword

nonn,easy,base

Author

Paolo P. Lava, May 18 2016

Extensions

a(16)-a(19) from Giovanni Resta, May 18 2016

Status

approved