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A083970 Numbers n such that concatenation (reverse of n) and n is divisible by n.

%I A083970 #29 Mar 28 2020 19:20:16
%S A083970 1,2,3,4,5,6,7,8,9,10,11,12,15,18,20,22,24,25,30,33,36,40,44,45,48,50,
%T A083970 55,60,66,70,75,77,80,88,90,99,100,101,110,111,120,121,125,131,132,
%U A083970 141,150,151,161,165,168,171,180,181,191,198,200,202,212,220,222,225,232
%N A083970 Numbers n such that concatenation (reverse of n) and n is divisible by n.
%C A083970 From _Sam Alexander_, Oct 21 2003: (Start)
%C A083970 All palindromes (in decimal) occur in this sequence. If we can multiply a(k) by j without having to resort to any carrying over, then ja(k) is also in the sequence.
%C A083970 Saying that R(n) concat n is divisible by n is equivalent to saying that (10^d)R(n) is divisible by n, where d = the number of digits in n. (End)
%C A083970 Contains A008919. - _Robert Israel_, Jul 27 2015
%H A083970 Robert Israel, <a href="/A083970/b083970.txt">Table of n, a(n) for n = 1..10000</a>
%e A083970 12 is a member as 2112 is divisible by 12 and 13 is not as 3113 is not divisible by 13.
%p A083970 filter:= proc(n) local L,m,i,v;
%p A083970     L:= convert(n,base,10);
%p A083970      m:= nops(L);
%p A083970     v:= add(10^(2*m-i)*L[i],i=1..m);
%p A083970     evalb(v mod n = 0);
%p A083970 end proc:
%p A083970 select(filter, [$1..10000]); # _Robert Israel_, Jul 26 2015
%t A083970 Select[ Range[ 250 ],
%t A083970 Divisible[
%t A083970    FromDigits[
%t A083970     Flatten[ { Reverse[ IntegerDigits[ # ] ] ,
%t A083970       IntegerDigits[ # ] } ] ], # ] & ]
%t A083970 (* _Kevin Southwick_, Jul 25 2015 *)
%t A083970 Select[Range[250],Divisible[IntegerReverse[#]*10^IntegerLength[#]+#,#]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 28 2020 *)
%Y A083970 Cf. A008919, A071273, A083971.
%K A083970 base,nonn
%O A083970 1,2
%A A083970 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 21 2003
%E A083970 Corrected and extended by _Sam Alexander_, Oct 21 2003