A193306 - OEIS

%I #14 Aug 01 2019 01:13:28

%S 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,

%T -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,

%U -1,3,6,-1,4,-1,-1,1,2,1,2,-1,-1,-1,-1,3,2,1,2

%N 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.

%H Kerry Mitchell, <a href="/A193306/b193306.txt">Table of n, a(n) for n = 0..10000</a>

%H W. J. Gilbert, <a href="http://www.jstor.org/stable/2689587">Arithmetic in Complex Bases</a>, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.

%e 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.

%Y Cf A193239, number of steps needed to reach a palindrome with complex base -1+i. 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.

%K sign,base

%O 0,3

%A _Kerry Mitchell_, Jul 22 2011