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Least number k = concat(x,y) such that k = n*x*y - x - y, -1 if such a number does not exist.
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%I #14 Dec 06 2016 22:04:53

%S 126,84,63,3231,42,4154,2143,1143,4105263158,6440909347642,21,11,2077,

%T 1077,18063,1206,16056,105882353,2052631579,43304763,3220454673821,

%U 8044,12042,30411,6039,5037593985,321603571507896,5035,14033492823,3033,17403126122889,20713030303119

%N Least number k = concat(x,y) such that k = n*x*y - x - y, -1 if such a number does not exist.

%C MSD of y can be 0.

%H Giovanni Resta, <a href="/A278935/a278935.txt">terms a(2)-a(100) which are smaller than 10^50</a>

%e a(5) = 3231 = concat(3,231) and 5*3*231 - 3 - 231 = 3231;

%e a(18) = 16056 = concat(16,056) and 18*16*56 - 16 - 56 = 16056.

%p with(numtheory): P:=proc(q) local j,k,s,t,n,ok;

%p for j from 2 to q do ok:=1; for n from 1 to q do if ok=0 then break; else

%p for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k);

%p if j*s*t-s-t=n then print(n); ok:=0; break; fi; od; fi; od; od; end: P(10^6);

%Y Cf. A279058.

%K nonn,base,more

%O 2,1

%A _Paolo P. Lava_, Dec 02 2016

%E a(10), a(11), a(19)-a(22), a(27), a(28), a(30), a(32), a(33) by _Giovanni Resta_, Dec 05 2016