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.

1, 3, 4, 5, 13, 21, 37, 40, 71, 82, 150, 140, 232, 252, 327, 352, 520, 497, 711, 729, 881, 1027, 1325, 1214, 1567, 1700, 1904, 2016, 2388, 2523, 2997, 3178, 3583, 3758, 4406, 4244, 5138, 5379, 6055, 5948, 6988, 7027, 8150, 8240, 8971, 9303, 10476, 10441, 11808, 12088, 13139, 13571, 15009, 15047, 16473, 16620, 18263, 19020

Offset: 1

Author

Dylan Hamilton, Jun 26 2012

Keywords

• nonn
• base

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

rev[x_,b_]:=FromDigits[Reverse[IntegerDigits[x,b]],b];Total/@Union/@Table[Table[rev[x,b],{b,2,x+1}],{x,Startpoint,Endpoint}]

PARI

rev(n,B)=my(m=n%B);n\=B;while(n>0,m=m*B+n%B;n\=B);m
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