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A116309 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3.

%I A116309 #17 Jul 17 2021 01:44:12
%S A116309 40,58,32262232,67737766,79321056,3341093417798787499093,
%T A116309 3861488851737861033961,4747922651210186579787,5252077348789813420211,
%U A116309 6138511148262138966037,6658906582201212500905,7232275368591793618231
%N A116309 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3.
%H A116309 Robert Israel, <a href="/A116309/b116309.txt">Table of n, a(n) for n = 1..67</a>
%H A116309 Robert Israel, <a href="/A116309/a116309.txt">Maple program used to obtain b-file</a>
%e A116309 79321056 * 79321059 = 62918301//62918304, where // denotes concatenation.
%p A116309 As:= {}:
%p A116309 for m from 2 to 62 do
%p A116309    acands:= map(t -> rhs(op(t)), [msolve(a*(a+3)=3, 10^m+1)]);
%p A116309    bcands:= map(t -> t*(t+3) mod 10^m, acands);
%p A116309    good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);
%p A116309    As:= As union convert(acands[good],set);
%p A116309 od:
%p A116309 sort(convert(As,list)); # _Robert Israel_, Aug 20 2019
%Y A116309 Cf. A116112, A116302, A116308, A116310, A116316.
%K A116309 nonn,base
%O A116309 1,1
%A A116309 _Giovanni Resta_, Feb 06 2006