A116295 Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+1.

8873, 9010, 83352841, 99000100, 329767122287, 670232877712, 738226276372, 933006600340, 999000001000, 3779410975143114, 3872816717528066, 4250291784692549, 4278630943941866, 4372036686326818, 4749511753491301

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Comments

From Robert Israel, Jun 06 2018: (Start)

Numbers k such that 10^m+1 | (k+1)^2-2 where (k+1)^2 has 2*m digits.

Includes 10^i - 10^(3*i) + 10^(4*i) for all i >= 1. (End)

Examples

			99000100 * 99000102 = 98010199//98010200, where // denotes concatenation.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A115426, A116286, A116294, A116296, A116308.

Programs

Maple

Res:= NULL:
for d from 1 to 40 do
  Res:= Res, op(sort(select(t -> t^2 >= 10^(2*d-1),map(t -> rhs(op(t))-1,[msolve(x^2=2, 10^d+1)]))))
od:
Res; # Robert Israel, Jun 06 2018