A083971 - OEIS

%I #32 Aug 06 2015 03:30:03

%S 11,11,11,11,11,11,11,11,11,11,101,176,341,451,11,101,176,209,11,101,

%T 176,11,101,121,176,11,101,11,101,11,77,101,11,101,11,101,11,1001,101,

%U 1001,176,1001,4169,1001,1751,1001,341,1001,1001,3401,5126,1001,451,1001,1001,4501,11,1001,1001

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

%H Robert Israel, <a href="/A083971/b083971.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%p f:= proc(n) local L,m,i,v;

%p     L:= convert(n,base,10);

%p      m:= nops(L);

%p     v:= add(10^(2*m-i)*L[i],i=1..m)/n+1;

%p     if v::integer then v else NULL fi

%p end proc:

%p map(f, [$1..1000]); # _Robert Israel_, Jul 26 2015

%t A083970 =

%t   Select[ Range[ 250 ],

%t    Divisible[

%t      FromDigits[

%t       Flatten[ { Reverse[ IntegerDigits[ # ] ], IntegerDigits[ # ] } ] ], # ] & ];

%t Table[ FromDigits[

%t    Flatten[ { Reverse[ IntegerDigits[ tmp ] ], IntegerDigits[ tmp ] } ] ] /

%t   tmp, {tmp, A083970} ]

%t (* _Kevin Southwick_, Jul 26 2015 *)

%Y Cf. A071273, A083970.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 21 2003

%E Corrected and extended by _Sam Alexander_, Oct 21 2003

%E Name edited by _Charles R Greathouse IV_, Aug 05 2015