A083971 Reverse of k concatenated with k, divided by k, where k = A083970(n).

11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 101, 176, 341, 451, 11, 101, 176, 209, 11, 101, 176, 11, 101, 121, 176, 11, 101, 11, 101, 11, 77, 101, 11, 101, 11, 101, 11, 1001, 101, 1001, 176, 1001, 4169, 1001, 1751, 1001, 341, 1001, 1001, 3401, 5126, 1001, 451, 1001, 1001, 4501, 11, 1001, 1001

Offset: 1

Author

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

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A071273, A083970.

Programs

Maple

f:= 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)/n+1;
    if v::integer then v else NULL fi
end proc:
map(f, [$1..1000]); # Robert Israel, Jul 26 2015

Mathematica

A083970 =
  Select[ Range[ 250 ],
   Divisible[
     FromDigits[
      Flatten[ { Reverse[ IntegerDigits[ # ] ], IntegerDigits[ # ] } ] ], # ] & ];
Table[ FromDigits[
   Flatten[ { Reverse[ IntegerDigits[ tmp ] ], IntegerDigits[ tmp ] } ] ] /
  tmp, {tmp, A083970} ]
(* Kevin Southwick, Jul 26 2015 *)

Formula

Note that when n is a palindrome, R(n)=n, so R(n) concat n = (10^d)n + n, where d is the number of digits of n, and R(n) is the reverse of n. Dividing by n, we obtain (R(n) concat n)/n = 10^d + 1. - Sam Alexander, Oct 21 2003; edited by Kevin Southwick, Jul 26 2015

Extensions

Corrected and extended by Sam Alexander, Oct 21 2003

Name edited by Charles R Greathouse IV, Aug 05 2015