A116309 - OEIS

%I #17 Jul 17 2021 01:44:12

%S 40,58,32262232,67737766,79321056,3341093417798787499093,

%T 3861488851737861033961,4747922651210186579787,5252077348789813420211,

%U 6138511148262138966037,6658906582201212500905,7232275368591793618231

%N Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3.

%H Robert Israel, <a href="/A116309/b116309.txt">Table of n, a(n) for n = 1..67</a>

%H Robert Israel, <a href="/A116309/a116309.txt">Maple program used to obtain b-file</a>

%e 79321056 * 79321059 = 62918301//62918304, where // denotes concatenation.

%p As:= {}:

%p for m from 2 to 62 do

%p    acands:= map(t -> rhs(op(t)), [msolve(a*(a+3)=3, 10^m+1)]);

%p    bcands:= map(t -> t*(t+3) mod 10^m, acands);

%p    good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);

%p    As:= As union convert(acands[good],set);

%p od:

%p sort(convert(As,list)); # _Robert Israel_, Aug 20 2019

%Y Cf. A116112, A116302, A116308, A116310, A116316.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006