A193306 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the reversed number from original.
0, 1, 2, 1, 4, 1, 4, 1, 4, 1, 4, 3, -1, -1, 4, 1, -1, 1, 4, -1, -1, 1, 4, -1, 2, 11, -1, 1, 2, 11, -1, 1, -1, 1, 12, 11, -1, 3, 2, -1, 6, -1, -1, -1, -1, 1, 12, 11, 4, -1, -1, 1, 8, 5, -1, 3, -1, 3, 6, -1, 4, -1, -1, 1, 2, 1, 2, -1, -1, -1, -1, 3, 2, 1, 2
Offset: 0
Examples
Decimal 2 is 10 in binary, which is -1+i using complex base -1+i. Reversing 10 gives 01, or 1+0i. Subtracting the reversed from the original results in -2+i, or 11111 using the complex base. Its reversal is the same, so subtracting them gives 0. Decimal 2 took 2 steps to reach 0, so a(2) = 2.
Links
- Kerry Mitchell, Table of n, a(n) for n = 0..10000
- W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.