cp's OEIS Frontend

A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x.

%I A308527 #13 Jun 20 2019 03:04:32
%S A308527 321,432,121110,171615,343332,118117116,232231230,334333332,
%T A308527 333433333332,452245214520,333343333333332,333334333333333332,
%U A308527 333333433333333333332,333333343333333333333332
%N A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x.
%C A308527 For each d>=1, (10^(3*d)-4)/3+10^(2*d) (the concatenation of x+2, x+1 and x where x = (10^d-4)/3) is in the sequence, being divisible by x+1 and x+3.  Thus the sequence is infinite.
%C A308527 It appears that a(n) is of the form (10^(3*d)-4)/3+10^(2*d) for n >= 11. - _Chai Wah Wu_, Jun 19 2019
%H A308527 Chai Wah Wu, <a href="/A308527/b308527.txt">Table of n, a(n) for n = 1..56</a>
%e A308527 232231230 is the concatenation of 232, 231 and 230, and is divisible by 231 and 230, so it is in the sequence.
%p A308527 f:=  proc(x)
%p A308527   local t1, t2, q, a, b;
%p A308527   t1:= 10^length(x);
%p A308527   t2:= t1*10^length(x+1);
%p A308527   q:= x*(1+t1+t2)+2*t2+t1;
%p A308527     a:= (q/x)::integer;
%p A308527   b:= (q/(x+1))::integer;
%p A308527   if a and b then return q elif not(a) and not(b) then return NULL fi;
%p A308527   if (q/(x+2))::integer then q else NULL fi
%p A308527 end proc:
%p A308527 map(f, [$1..10^8]);
%Y A308527 Cf. A306643.
%Y A308527 Subsequence of A127424.
%K A308527 nonn,base
%O A308527 1,1
%A A308527 _J. M. Bergot_ and _Robert Israel_, Jun 05 2019