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A211518 a(n) is the sum of all distinct integers that can be produced by reversing the digits of n in any base b >= 2.

%I A211518 #25 May 13 2013 01:54:21
%S A211518 1,3,4,5,13,21,37,40,71,82,150,140,232,252,327,352,520,497,711,729,
%T A211518 881,1027,1325,1214,1567,1700,1904,2016,2388,2523,2997,3178,3583,3758,
%U A211518 4406,4244,5138,5379,6055,5948,6988,7027,8150,8240,8971,9303,10476,10441,11808,12088,13139,13571,15009,15047,16473,16620,18263,19020
%N A211518 a(n) is the sum of all distinct integers that can be produced by reversing the digits of n in any base b >= 2.
%H A211518 Charles R Greathouse IV, <a href="/A211518/b211518.txt">Table of n, a(n) for n = 1..10000</a>
%e A211518 If n=3, we can get 3 from base 10 (or any other base except 3) and 1 from reversing the base-3 expansion 10, so a(3) = 3+1 = 4.
%t A211518 rev[x_,b_]:=FromDigits[Reverse[IntegerDigits[x,b]],b];Total/@Union/@Table[Table[rev[x,b],{b,2,x+1}],{x,Startpoint,Endpoint}]
%o A211518 (PARI) rev(n,B)=my(m=n%B);n\=B;while(n>0,m=m*B+n%B;n\=B);m
%o A211518 a(n)=if(n<3,2*n-1,my(v=vecsort(vector(n-1,k,rev(n,k+1)),,8));sum(i=1,#v,v[i])) \\ _Charles R Greathouse IV_, Aug 05 2012
%K A211518 nonn,base
%O A211518 1,2
%A A211518 _Dylan Hamilton_, Jun 26 2012