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

1,2

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A008919, A071273, A083971.

Sequence in context: A263808 A180477 A271239 * A246088 A071204 A002796

Adjacent sequences: A083967 A083968 A083969 * A083971 A083972 A083973

Keyword

base,nonn

Author

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

Extensions

Corrected and extended by Sam Alexander, Oct 21 2003

Status

approved