A008919 -id:A008919 - cp's OEIS frontend

A082945 Numbers n which in decimal have the form imj, where m is the middle digit, with property that j is the reversal of i, and i = m*j.

111, 212, 313, 414, 515, 616, 717, 818, 919, 11111, 22122, 33133, 44144, 55155, 66166, 77177, 88188, 99199, 1011101, 1111111, 1211121, 1311131, 1411141, 1511151, 1611161, 1711171, 1811181, 1911191, 2021202, 2121212, 2221222, 2321232, 2421242

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 07 2003

The number i should not end in 0, and m should not equal 0.
Suggested by Amarnath Murthy.
Either i and j are identical palindromes and m is 1, or i is in A031877, j is the corresponding term in A008919, and m is either 4 or 9. - Charlie Neder, Mar 08 2019

			rev(8712) = 2178 and 8712 = 2178*4, so 871242178 is in this sequence. - _Charlie Neder_, Mar 08 2019

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A002113, A008919, A031877. (Possible values of i and j)

Edited by N. J. A. Sloane, Oct 25 2009, following discussions on the Sequence Fans Mailing List, circa Apr 17 2009

Corrected and extended by Charlie Neder, Mar 08 2019

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

Original entry on oeis.org

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

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

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

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

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

Cf. A008919, A071273, A083971.

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

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 *)

Corrected and extended by Sam Alexander, Oct 21 2003

cp's OEIS Frontend

A082945 Numbers n which in decimal have the form imj, where m is the middle digit, with property that j is the reversal of i, and i = m*j.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions