A193239 - OEIS

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

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OFFSET

0,12

COMMENTS

N is converted to its binary representation before iterating.

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.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A094774 A231925 A337464 * A023406 A138116 A348999

Adjacent sequences: A193236 A193237 A193238 * A193240 A193241 A193242

KEYWORD

base,sign

AUTHOR

Kerry Mitchell, Jul 19 2011

STATUS

approved