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%I #14 Jul 18 2021 02:55:49
%S 8873,9010,83352841,99000100,329767122287,670232877712,738226276372,
%T 933006600340,999000001000,3779410975143114,3872816717528066,
%U 4250291784692549,4278630943941866,4372036686326818,4749511753491301
%N Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+1.
%C From _Robert Israel_, Jun 06 2018: (Start)
%C Numbers k such that 10^m+1 | (k+1)^2-2 where (k+1)^2 has 2*m digits.
%C Includes 10^i - 10^(3*i) + 10^(4*i) for all i >= 1. (End)
%H Robert Israel, <a href="/A116295/b116295.txt">Table of n, a(n) for n = 1..600</a>
%e 99000100 * 99000102 = 98010199//98010200, where // denotes concatenation.
%p Res:= NULL:
%p for d from 1 to 40 do
%p 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)]))))
%p od:
%p Res; # _Robert Israel_, Jun 06 2018
%Y Cf. A115426, A116286, A116294, A116296, A116308.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 06 2006
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