A116129 Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 4.

11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Comments

From Robert Israel, Aug 13 2018: (Start)

Contains, and appears to be identical to, A116098.

Numbers k such that (10^d+1)*k is a square, where k-4 has d digits. (End)

Examples

			100000001//99999997 = 99999999 * 100000003, where // denotes concatenation.
		

Crossrefs

Cf. A116098, A054214, A116128, A116130, A116136, A116260.

Programs

Maple

g:= proc(d) local r,c,a,b;
   r:= mul(t[1],t=select(s -> s[2]::odd, ifactors(10^d+1)[2]));
   c:= ceil((10^(d-1)+4)/r);
   a:= isqrt(c);
   if a^2 < c then a:= a+1 fi;
   c:= floor((10^d+3)/r);
   b:= isqrt(c);
   if b^2 > c then b:= b-1 fi;
   seq(r*y^2, y = a..b)
end proc:
map(g, [$1..60]); # Robert Israel, Aug 13 2018