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A116170 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 1.

%I A116170 #9 Jul 20 2021 23:46:48
%S A116170 590,738,830,1080,4508,20660,29754,980300,6694218,49826988,117738578,
%T A116170 131505858,132231404,176445054,177285320,247979808,252028388,
%U A116170 335180054,336337790,404958680,406231130,431477468,499519478
%N A116170 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 1.
%H A116170 Robert Israel, <a href="/A116170/b116170.txt">Table of n, a(n) for n = 1..9000</a>
%p A116170 As:= {}:
%p A116170 for m from 2 to 20 do
%p A116170    acands:= map(t -> rhs(op(t)), [msolve(a*(a+1)=2, 10^m+1)]);
%p A116170    bcands:= map(t -> t*(t+1) mod 10^m, acands);
%p A116170    good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);
%p A116170    As:= As union convert(bcands[good], set);
%p A116170 od: map(t -> t-2, sort(convert(As, list))); # _Robert Israel_, Aug 20 2019
%Y A116170 Cf. A116163, A116171, A116099, A116301.
%K A116170 nonn,base
%O A116170 1,1
%A A116170 _Giovanni Resta_, Feb 06 2006