[seqfan] Re: Binary Complement Sequences

[Tom Duff]

The record-setting values of the number of steps (along with which starting
number gives that number of steps) up to 425719 are

1 1

2 2

3 11

4 12

9 13

11 19

12 80

17 81

23 83

28 7572

33 7573

74 7574

86 7578

180 7580

227 664475

350 664882

821 3180929

3822 3180930

4187 3180931

5561 3181981

6380 3181988

6398 3182002

22174 3182226

22246 120796790

26494 556068798

34859 556068799

49827 556068871

70772 556068872

103721 572086553

104282 572086610

204953 1246707529

213884 1246707552

225095 1246707555

407354 1246707602

The number of steps for 425720 is at least 16,943,000,000 -- still running
after 32 hours of CPU time on my M1 Mac Mini.

On Mon, Dec 19, 2022 at 7:14 PM Tim Peters <tim.peters at gmail.com> wrote:

> > Joshua Searle: "I can give you term 9,999,999,999 of seed 425720, or the
> step lengths/maxima of
> > sequences up to 425720 that didn’t get caught by my side-sequence
> filter."
> > Not sure what your filter filtered but I'm curious about what happens to
> 22246.
>
> > Hans Havermann: Not sure what your filter filtered but I'm curious about
> what happens to 22246.
>
> I can't speak for Joshua's code, but in my code that's the first "jaw
> dropping" starting value, taking 120,796,790 steps to reach 0, Ir
> nevertheless completes very much faster than 425720 (which is still
> slogging through values with about 400,000 bits after about 14 billion
> steps on my box so far). The max value reached from 22246 had a "mere"
> 27,596 bits.
>
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