%I #9 Jun 21 2024 03:51:27

%S 31,65,42754,57242,75424,425073,574923,979529,4301394,5698602,7028667,

%T 4925000748,5074999248,7748266575,8511881485,8814851185,7059602159673,

%U 7106167933829,7439286611622,7485852385778,46791112884926

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

%H Robert Israel, <a href="/A116324/b116324.txt">Table of n, a(n) for n = 1..5283</a>

%p f:= proc(d) local S,R,r,s,m,n;

%p r:= 10^d+1;

%p S:= map(t -> rhs(op(t)), [msolve(n*(n+5)=5,r)]);

%p 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 op(sort(S));

%p end proc:

%p map(f, [$1..20]); # _Robert Israel_, Jun 21 2024

%Y Cf. A028557, A032610.

%Y Cf. A116193, A116310, A116323, A116325, A116331.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006