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A116287 Numbers k such that k*(k+3) gives the concatenation of a number m with itself.

%I A116287 #18 Apr 09 2025 07:23:41
%S A116287 8,98,767,858,910,998,3285,6713,9998,45452,54546,99998,990100,999998,
%T A116287 8181819,9999998,70588233,99999998,343130554,362637363,363636361,
%U A116287 420053631,421052632,497975709,502024289,578947366,579946367,636363637,637362635,656869444,706766918,713286714,714285712,783689995
%N A116287 Numbers k such that k*(k+3) gives the concatenation of a number m with itself.
%C A116287 From _Robert Israel_, Apr 08 2025: (Start)
%C A116287 Numbers k such that k * (k + 3) = (10^d + 1) * m for some d and m where m has d digits.
%C A116287 Contains 10^d-2 for all d >= 1. (End)
%H A116287 Robert Israel, <a href="/A116287/b116287.txt">Table of n, a(n) for n = 1..10000</a>
%p A116287 q:= proc(d,m) local R,t,a,b,x,q;
%p A116287    t:= 10^d+1;
%p A116287    R:= NULL;
%p A116287    for a in numtheory:-divisors(t) do
%p A116287      b:= t/a;
%p A116287      if igcd(a,b) > 1 then next fi;
%p A116287      for x from chrem([0,-m],[a,b]) by t do
%p A116287        q:= x*(x+m)/t;
%p A116287        if q >= 10^d then break fi;
%p A116287        if q >= 10^(d-1) then R:= R, x fi;
%p A116287    od od;
%p A116287    sort(convert({R},list));
%p A116287 end proc:
%p A116287 seq(op(q(d,3)),d=1..10); # _Robert Israel_, Apr 08 2025
%Y A116287 Cf. A116130, A116280, A116286, A116288, A116296.
%K A116287 nonn,base
%O A116287 1,1
%A A116287 _Giovanni Resta_, Feb 06 2006
%E A116287 More terms from _Robert Israel_, Apr 08 2025