OFFSET
1,1
COMMENTS
Any number ends in 9.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
9 - 8*1 = 1 = 1^2;
889249 - 8*111111 = 361 = 19^2;
896809 - 8*111111 = 7921 = 89^2.
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, 8);
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_] := 8 (10^n-1)/9; Flatten[sol /@ r /@ Range[12]] (* Giovanni Resta, May 18 2016 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, May 18 2016
EXTENSIONS
a(11)-a(17) from Giovanni Resta, May 18 2016
STATUS
approved