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A116324 Numbers k such that k * (k+5) gives the concatenation of two numbers m and m+5.

%I A116324 #9 Jun 21 2024 03:51:27
%S A116324 31,65,42754,57242,75424,425073,574923,979529,4301394,5698602,7028667,
%T A116324 4925000748,5074999248,7748266575,8511881485,8814851185,7059602159673,
%U A116324 7106167933829,7439286611622,7485852385778,46791112884926
%N A116324 Numbers k such that k * (k+5) gives the concatenation of two numbers m and m+5.
%H A116324 Robert Israel, <a href="/A116324/b116324.txt">Table of n, a(n) for n = 1..5283</a>
%p A116324 f:= proc(d) local S,R,r,s,m,n;
%p A116324   r:= 10^d+1;
%p A116324   S:= map(t -> rhs(op(t)), [msolve(n*(n+5)=5,r)]);
%p A116324   S:= select(proc(s) local t; t:= (s*(s+5)-5)/r; t+5 >= (r-1)/10 and t+5 < r-1 end proc, S);
%p A116324   op(sort(S));
%p A116324 end proc:
%p A116324 map(f, [$1..20]); # _Robert Israel_, Jun 21 2024
%Y A116324 Cf. A028557, A032610.
%Y A116324 Cf. A116193, A116310, A116323, A116325, A116331.
%K A116324 nonn,base
%O A116324 1,1
%A A116324 _Giovanni Resta_, Feb 06 2006