[seqfan] Re: Project: sequences obtained from Gaussian Integers via Penney's binary method of encoding?

Kevin Ryde user42_kevin at yahoo.com.au
Sat Sep 17 09:48:13 CEST 2016


zabolotis at mail.ru (Андрей Заболотский) writes:
>
> Well, I get 29, 28, 17, 16, 205, 204, 193, 192, 221, 220..., which is really A256441.

Oh yes that's n on negative X axis.  I was negating the complex z,
eg. with gp

  point(n)=subst(Pol(binary(n)),'x,I-1);
  point(5)  ==   1-2*I
  point(25) == -(1-2*I)

so n=5 negates as neg(5)=25, and vice versa neg(25)=5,
neg(n)=unpoint(-point(n)).

Looks like there's a pattern to the bit flips going n to neg(n), so that
bitxor(n,neg(n)) has 1-bits as runs 11100 or 100.  I imagine that would
follow from Khmelnik's table of how "borrow" propagates upwards.



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