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A116268 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-3.

%I A116268 #18 Jul 12 2025 18:45:43
%S A116268 81,77394227,89158933,36623663376237623663376335,
%T A116268 37633762366336633762366235,62366237633663366237633761,
%U A116268 63376336623762376336623661,86194223018927804587702128,88063202723646452838040443,35574229497606875609044578088011,35693849662968953146129859753682,42317841210726174031503123524229
%N A116268 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-3.
%H A116268 Robert Israel, <a href="/A116268/b116268.txt">Table of n, a(n) for n = 1..220</a>
%e A116268 89158933 * 89158938 = 79493157//79493154, where // denotes concatenation.
%p A116268 f:= proc(d) local k, K;
%p A116268       K:= map(t -> rhs(op(t)), [msolve(k^2+5*k+3=0,10^d+1)]);
%p A116268       op(sort(select(k -> k^2 + 5*k + 3 >= (10^d+1)*10^(d-1), K)));
%p A116268 end proc:
%p A116268 map(f, [$1..62]); # _Robert Israel_, Jul 10 2025
%Y A116268 Cf. A028557, A116099, A116261, A116267, A116269, A116276.
%K A116268 nonn,base
%O A116268 1,1
%A A116268 _Giovanni Resta_, Feb 06 2006
%E A116268 More terms from _Robert Israel_, Jul 10 2025