A193239 Number of "Reverse and Add" steps needed to reach a palindrome using the complex base -1+i, or -1 if a palindrome is never reached.

0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 6, 1, 6, 1, 0, 1, 0, 1, 4, -1, 0, -1, -1, 1, 4, -1, 0, -1, -1, 5, 0, 1, 0, 1, 6, 1, -1, 1, -1, 1, -1, 1, -1, -1, 0, 7, -1, 1, 6, 7, 0, 1, -1, 1, 2, 1, -1, 1, 2, 7, -1, -1, 0, 1, 0, 1, -1, 1, -1, 1, -1, 3, 0, -1, -1, 9, 2, 1

Offset: 0

Author

Kerry Mitchell, Jul 19 2011

Keywords

• base
• sign

Comments

N is converted to its binary representation before iterating.

Examples

			Decimal 2 is 10 in binary, which is -1+i using complex base -1+i. Reversing 10 gives 01, or 1+0i.  Adding both results in 0+i, or 11 using the complex base, which is a palindrome.  Decimal 2 took 1 step to reach a palindrome, so a(2) = 1.
		

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.

Crossrefs

Cf. A033665 gives the steps to reach a palindrome in base 10.