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A116293 Numbers k such that k * (k+9) is the concatenation of a number m with itself.

%I A116293 #9 Apr 09 2025 07:21:44
%S A116293 2,92,420,572,693,728,992,9855,9992,36355,63637,99992,970298,999992,
%T A116293 4545455,5454537,9999992,88235295,99999992,351069983,403018035,
%U A116293 493927126,506072866,596981957,648930009,736842097,739839100,766233767,769230761,827751188,857142858,860139852,879699240,909090910
%N A116293 Numbers k such that k * (k+9) is the concatenation of a number m with itself.
%C A116293 From _Robert Israel_, Apr 09 2025: (Start)
%C A116293 Numbers k such that k * (k + 9) = (10^d + 1) * m for some d and m where m has d digits.
%C A116293 Contains 10^d-8 for all d >= 1. (End)
%H A116293 Robert Israel, <a href="/A116293/b116293.txt">Table of n, a(n) for n = 1..10000</a>
%p A116293 q:= proc(d,m) local R,t,a,b,x,q;
%p A116293    t:= 10^d+1;
%p A116293    R:= NULL;
%p A116293    for a in numtheory:-divisors(t) do
%p A116293      b:= t/a;
%p A116293      if igcd(a,b) > 1 then next fi;
%p A116293      for x from chrem([0,-m],[a,b]) by t do
%p A116293        q:= x*(x+m)/t;
%p A116293        if q >= 10^d then break fi;
%p A116293        if q >= 10^(d-1) then R:= R, x fi;
%p A116293    od od;
%p A116293    sort(convert({R},list));
%p A116293 end proc:
%p A116293 seq(op(q(d,9)),d=1..10)
%Y A116293 Cf. A116162, A116284, A116292, A116300.
%K A116293 nonn,base
%O A116293 1,1
%A A116293 _Giovanni Resta_, Feb 06 2006
%E A116293 Name edited and more terms from _Robert Israel_, Apr 09 2025