A097151 - OEIS

%I #4 Mar 30 2012 17:36:43

%S 0,1,2,3,4,-5,1,-4,1,-3,1,-2,1,-1,1,0,1,1,1,2,1,3,1,4,1,-5,2,-4,2,-3,

%T 2,-2,2,-1,2,0,2,1,2,2,2,3,2,4,2,-5,3,-4,3,-3,3,-2,3,-1,3,0,3,1,3,2,3,

%U 3,3,4,3,-5,4,-4,4,-3,4,-2,4,-1,4,0,4,1,4,2,4,3,4,4,4,-5,-5,1,-4,-5,1,-3,-5,1,-2,-5,1,-1,-5,1,0,-5,1,1,-5,1,2,-5,1,3,-5,1

%N Digits of balanced base-10 representations of nonnegative integers (least significant digits first).

%C Definition 9.1.2. of the Crandall-Pomerance book is: "The balanced base-B representation of a nonnegative integer x is the shortest sequence of integer digits (x_i) such that each digit satisfies -floor(B/2) <= x_i <= floor((B-1)/2) and x = sum(i=0,D-1,x_i*B^i)." (I have replaced floor and sigma symbols with "floor" and "sum" for inclusion here.) The D digits x_0, x_1, x_2, ..., x_(D-1) are included in this order in this sequence and in the opposite order in A097150.

%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 408.

%e As the only digits permissible are in {-5,-4,-3,-2,-1,0,1,2,3,4},

%e 5 = -5 + 1*10 is the first number requiring two of these digits: -5,1.

%e A097150 is the same sequence but with the digits in reverse order.

%e Also, 45 = -5 - 5*10 + 1*10^2 has digits -5,-5,1,

%e 54 = 4 - 5*10 + 1*10^2 has digits 4,-5,1 and

%e 55 = -5 - 4*10 + 1*10^2 has digits -5,-4,1.

%Y Cf. A097150 (most significant digits first).

%K base,easy,sign

%O 1,3

%A _Rick L. Shepherd_, Jul 27 2004