A193307 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the original number from the reversed.
0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 2, 15, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 3, -1, 1, -1, 3, -1, 1, -1, 1, -1, 3, 2, -1, -1, 15, -1, -1, -1, -1, -1, 1, -1, 3, -1, -1, -1, 1, -1, 7, 2, -1, 2, -1, -1, -1, -1, -1, -1, 1, 14, 1, -1, -1, 6, -1, -1
Offset: 0
Examples
Decimal 12 is 1100 in binary, which is 2+0i using complex base -1+i. Reversing 1100 gives 0011, or 0+i. Subtracting the original number from the reversed results in -2+i, or 11111 using the complex base. Its reversal is the same, so subtracting them gives 0. Decimal 12 took 2 steps to reach 0, so a(12) = 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.
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