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

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, 55, 60, 66, 70, 75, 77, 80, 88, 90, 99, 100, 101, 110, 111, 120, 121, 125, 131, 132, 141, 150, 151, 161, 165, 168, 171, 180, 181, 191, 198, 200, 202, 212, 220, 222, 225, 232

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 21 2003

Keywords

• base
• nonn

Comments

From Sam Alexander, Oct 21 2003: (Start)

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.

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)

Contains A008919. - Robert Israel, Jul 27 2015

Examples

			12 is a member as 2112 is divisible by 12 and 13 is not as 3113 is not divisible by 13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008919, A071273, A083971.

Programs

Maple

filter:= proc(n) local L,m,i,v;
    L:= convert(n,base,10);
     m:= nops(L);
    v:= add(10^(2*m-i)*L[i],i=1..m);
    evalb(v mod n = 0);
end proc:
select(filter, [$1..10000]); # Robert Israel, Jul 26 2015

Mathematica

Select[ Range[ 250 ],
Divisible[
   FromDigits[
    Flatten[ { Reverse[ IntegerDigits[ # ] ] ,
      IntegerDigits[ # ] } ] ], # ] & ]
(* Kevin Southwick, Jul 25 2015 *)
Select[Range[250],Divisible[IntegerReverse[#]*10^IntegerLength[#]+#,#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 28 2020 *)

Extensions

Corrected and extended by Sam Alexander, Oct 21 2003