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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. 2

%I

%S 321,432,121110,171615,343332,118117116,232231230,334333332,

%T 333433333332,452245214520,333343333333332,333334333333333332,

%U 333333433333333333332,333333343333333333333332

%N 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 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 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 Chai Wah Wu, <a href="/A308527/b308527.txt">Table of n, a(n) for n = 1..56</a>

%e 232231230 is the concatenation of 232, 231 and 230, and is divisible by 231 and 230, so it is in the sequence.

%p f:= proc(x)

%p local t1, t2, q, a, b;

%p t1:= 10^length(x);

%p t2:= t1*10^length(x+1);

%p q:= x*(1+t1+t2)+2*t2+t1;

%p a:= (q/x)::integer;

%p b:= (q/(x+1))::integer;

%p if a and b then return q elif not(a) and not(b) then return NULL fi;

%p if (q/(x+2))::integer then q else NULL fi

%p end proc:

%p map(f, [$1..10^8]);

%Y Cf. A306643.

%Y Subsequence of A127424.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jun 05 2019

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)