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A116345 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.

%I A116345 #13 Jul 17 2021 01:44:54
%S A116345 41,54,40354308,59645687,39704957106129738595969799927611,
%T A116345 44505281604832422780051712184760,45053875613995255103944518907120,
%U A116345 54946124386004744896055481092875,55494718395167577219948287815235,60295042893870261404030200072384,68683652917306421895276391964227
%N A116345 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.
%H A116345 Robert Israel, <a href="/A116345/b116345.txt">Table of n, a(n) for n = 1..41</a>
%e A116345 59645687 * 59645693 = 35576083//35576091, where // denotes concatenation.
%p A116345 f:= proc(d) local R;
%p A116345    R:= map(rhs@op,{msolve(x^2=17,10^d+1)});
%p A116345    R:= map(t -> (t-3) mod (10^d+1), R);
%p A116345    op(select(proc(t) local m; m:= (t*(t+6)-8)/(10^d+1)+8; m >= 10^(d-1) and m < 10^d end proc, R));
%p A116345 end proc;
%p A116345 sort(convert({seq(f(i),i=1..50)},list)); # _Robert Israel_, Jan 17 2017
%Y A116345 Cf. A116168, A116339, A116344, A116346, A116352.
%K A116345 nonn,base
%O A116345 1,1
%A A116345 _Giovanni Resta_, Feb 06 2006
%E A116345 More terms from _Robert Israel_, Jan 17 2017