8, 8 days until Disney! Ah ha ha!

[bump] Powers of 2 base 7

The largest power of two that does not have three consecutive 0's in its base 7 representation is possibly this number:

  20 41555 56212 50216 62652 23252 46103 30020 62254 60111 51005 30646
56141 02033 64434 35400 65340 63154 21162 60506 45026 56202 02346 61015
02006 40446 54031 23411 45226 52345 41621 52033 51326 40352 66200 46230
32060 31410 10144 41325 10346 55250 16514 02552 21643 50631 50223 50342
20642 50643 14555 25023 32443 02352 65521 30552 02004 06420 01121 43306
55612 36052 51031 56035 43015 46463 15635 46255 05412 36100 46632 26560
12030 06646 34312 01500 60423 34516 34321 14141 40411 31630 02443 33050
26364 02310 36424 25030 03255 15635 45401 11541 33346 22305 06002 26255
02561 14141 62441 25555 31522 23211 35450 03540 22451 51513 32503 36342
56602 35201 32351 53205 11066 52212 24056 43262 42533 32551 64221 55352
66342 61003 15414 62021 40061 54563 24135 03522 04103 03405 33010 26311
34114 02155 66411 32311 12032 21424 42605 61652 51655 13516 64150 02460
06026 06642 44344 25302 60456 04464 50605 55261 44340 03310 64123 03620
32624 05625 31040 44362 02324 64150 43413 25064 65105 32653 04345 42442
21235 04622 43211 14303 14405 31620 12333 06421 60222 64545 12010 51603
56405 62511 16521 31552 66601 13336 21646 52204 65120 63413 20630 62405
43011 15526 25121 43512 65353 00162 65566 16660 60432 01433 35506 54612
05442 31316 25462 13342 04014 42042 62626 33215 05500 10034 26204 43160
35364 23141 23230 31054 52014 41256 33024 11413 45655 33510 03324 06533
30252 25415 51121 04624 14645 56442 21400 42032 11125 43444 65421 51624
25423 31325 16436 36311 66355 25126 41623 55340 35050 33430 20562 42433
03254 42142 62510 31263 13112 63556 46425 50436 03051 62051 61664 03515
60366 04252 52334 20604 23242 41430 05616 53625 41602 40113 23140 41245
50102 62361 63006 62550 35251 61430 63414 32232 53354 11116 45011 11251
01166 22061 43605 54334 21355 03063 45002 45151 41032 24356 30114 11110
06305 00530 02403 25462 03411 53320 22451 64340 01633 33546 00360 53235
03051 20550 11536 61145 34612 03334 36331 34304 41215 32613 40122 34436
66555 33644 25543 42526 43510 46326 21540 41231 44140 35562 00400 32310
52400 56160 64216 46412 56611 25244 16463 35034 16161 21350 36564 14014
53432 41242 56521 65456 31316 33115 06161 63635 62041 13204 04652 13235
64323 56061 41661 31605 52161 44410 15256 65361 15204 66045 35635 43036
00161 06206 34053 26102 23313 35030 41453 50154 61664 36040 51144 43062
54001 55266 02264 43164 10222 63456 13562 16224 55313 54543 20132 44512
21515 43316 40360 30063 30566 01254 15644 14211 23010 46412 30423 34011
05661 43561 41122 65312 00654 56556 35516 10065 13525 51454 16566 61231
33655 14343 63365 31302 25165 12206 52336 52031 56112 04332 05663 21650
52101 42211 14200 22256 00650 60131 16255 13564 11631 41651 40053 55043
54165 60516 42225 02336 52265 12332 22134 30404 13343 00365 12253 30354
25334 44562 16506 65652 00222 66331 53643 33131 23164 55352 50615 32326
65526 05130 11300 21306 14252 15113 43646 32304 35440 66664 53364 23026
11160 14150 32131 04621 31024 50056 33365 30562 30362 55245 60212 13160
40634 05153 56462 16653 62310 15260 36534 42664 02230 55460 13101 51243
35010 51136 33251 43415 40536 52022 54446 56433 44566 15121 25630 11565
35465 06546 53101 55110 20353 51101 01565 32612 13146 33542 02153 03400
14514 46300 65654 51121 64542 21410 05056 04522 50632 33126 01165 53041
44650 13101 51326 03544 22256 51545 61620 20042 04301 54352 51612 36053
42302 00344 61025 04553 23145 20265 21455 16554 35066 26646 53161 35443
63230 61632 52352 05040 64053 62223 44202 10525 55401 66113 33465 11230
63246 56040 02646 41311 36160 43046 06032 63225 36125 06645 63056 22213
61451 00215 61335 55521 65644 11666 45215 20615 01662 01321 60261 33633
20050 64032 54142 62424 50641 64221 00444 00143 31126 60131 23423 00600
15654 04655 01665 36662 54346 06340 63002 24350 16544 31165 10314 05520
66602 45045 15031 51126 26361 63612

Fascinating that there might even be a largest such number. So the question is, can anyone find a bigger one?
Permalink Send private email bon vivant 
April 5th, 2007 5:59pm
Stupid word wrapping. Did nobody hear of a standard 80 character line length these days?
Permalink Send private email bon vivant 
April 5th, 2007 6:01pm
With no funny wrapping:

  20 41555 56212 50216 62652 23252 46103 30020
62254 60111 51005 30646 56141 02033 64434 35400
65340 63154 21162 60506 45026 56202 02346 61015
02006 40446 54031 23411 45226 52345 41621 52033
51326 40352 66200 46230 32060 31410 10144 41325
10346 55250 16514 02552 21643 50631 50223 50342
20642 50643 14555 25023 32443 02352 65521 30552
02004 06420 01121 43306 55612 36052 51031 56035
43015 46463 15635 46255 05412 36100 46632 26560
12030 06646 34312 01500 60423 34516 34321 14141
40411 31630 02443 33050 26364 02310 36424 25030
03255 15635 45401 11541 33346 22305 06002 26255
02561 14141 62441 25555 31522 23211 35450 03540
22451 51513 32503 36342 56602 35201 32351 53205
11066 52212 24056 43262 42533 32551 64221 55352
66342 61003 15414 62021 40061 54563 24135 03522
04103 03405 33010 26311 34114 02155 66411 32311
12032 21424 42605 61652 51655 13516 64150 02460
06026 06642 44344 25302 60456 04464 50605 55261
44340 03310 64123 03620 32624 05625 31040 44362
02324 64150 43413 25064 65105 32653 04345 42442
21235 04622 43211 14303 14405 31620 12333 06421
60222 64545 12010 51603 56405 62511 16521 31552
66601 13336 21646 52204 65120 63413 20630 62405
43011 15526 25121 43512 65353 00162 65566 16660
60432 01433 35506 54612 05442 31316 25462 13342
04014 42042 62626 33215 05500 10034 26204 43160
35364 23141 23230 31054 52014 41256 33024 11413
45655 33510 03324 06533 30252 25415 51121 04624
14645 56442 21400 42032 11125 43444 65421 51624
25423 31325 16436 36311 66355 25126 41623 55340
35050 33430 20562 42433 03254 42142 62510 31263
13112 63556 46425 50436 03051 62051 61664 03515
60366 04252 52334 20604 23242 41430 05616 53625
41602 40113 23140 41245 50102 62361 63006 62550
35251 61430 63414 32232 53354 11116 45011 11251
01166 22061 43605 54334 21355 03063 45002 45151
41032 24356 30114 11110 06305 00530 02403 25462
03411 53320 22451 64340 01633 33546 00360 53235
03051 20550 11536 61145 34612 03334 36331 34304
41215 32613 40122 34436 66555 33644 25543 42526
43510 46326 21540 41231 44140 35562 00400 32310
52400 56160 64216 46412 56611 25244 16463 35034
16161 21350 36564 14014 53432 41242 56521 65456
31316 33115 06161 63635 62041 13204 04652 13235
64323 56061 41661 31605 52161 44410 15256 65361
15204 66045 35635 43036 00161 06206 34053 26102
23313 35030 41453 50154 61664 36040 51144 43062
54001 55266 02264 43164 10222 63456 13562 16224
55313 54543 20132 44512 21515 43316 40360 30063
30566 01254 15644 14211 23010 46412 30423 34011
05661 43561 41122 65312 00654 56556 35516 10065
13525 51454 16566 61231 33655 14343 63365 31302
25165 12206 52336 52031 56112 04332 05663 21650
52101 42211 14200 22256 00650 60131 16255 13564
11631 41651 40053 55043 54165 60516 42225 02336
52265 12332 22134 30404 13343 00365 12253 30354
25334 44562 16506 65652 00222 66331 53643 33131
23164 55352 50615 32326 65526 05130 11300 21306
14252 15113 43646 32304 35440 66664 53364 23026
11160 14150 32131 04621 31024 50056 33365 30562
30362 55245 60212 13160 40634 05153 56462 16653
62310 15260 36534 42664 02230 55460 13101 51243
35010 51136 33251 43415 40536 52022 54446 56433
44566 15121 25630 11565 35465 06546 53101 55110
20353 51101 01565 32612 13146 33542 02153 03400
14514 46300 65654 51121 64542 21410 05056 04522
50632 33126 01165 53041 44650 13101 51326 03544
22256 51545 61620 20042 04301 54352 51612 36053
42302 00344 61025 04553 23145 20265 21455 16554
35066 26646 53161 35443 63230 61632 52352 05040
64053 62223 44202 10525 55401 66113 33465 11230
63246 56040 02646 41311 36160 43046 06032 63225
36125 06645 63056 22213 61451 00215 61335 55521
65644 11666 45215 20615 01662 01321 60261 33633
20050 64032 54142 62424 50641 64221 00444 00143
31126 60131 23423 00600 15654 04655 01665 36662
54346 06340 63002 24350 16544 31165 10314 05520
66602 45045 15031 51126 26361 63612

Can't help the variable width font though.
Permalink Send private email bon vivant 
April 5th, 2007 6:07pm
Yep.
Permalink Practical Economist 
April 5th, 2007 6:17pm
and what does this piece of info serves for?
Permalink Tony MBA 
April 5th, 2007 6:17pm
How high did you go above that number?
Permalink Send private email strawberry snowflake 
April 5th, 2007 6:19pm
(Tony, reference this thread: http://www.crazyontap.com/topic.php?TopicId=17288 )

I went up to 2^30000, but I reckon it would need a search up to 2^1000000 to start feeling confident there really might be a largest such number.
Permalink Send private email bon vivant 
April 5th, 2007 6:22pm
Doesn't matter how high you go - I need a proof goddammit!!!
Permalink bob's your uncle 
April 5th, 2007 6:26pm
yeah, I went to the gym and left it running. it got to 2^27000 and stalled for some reason. that was good enough. I was happier that I discovered a couple optimization techniques right off the bat and stuck the in.
Permalink Send private email strawberry snowflake 
April 5th, 2007 6:28pm
Well, use this thread to start constructing a proof.
Permalink Send private email bon vivant 
April 5th, 2007 6:29pm
Went to the gym? I did a quick Perl hack and it took about two minutes up to 30,000. What did you code yours in?
Permalink Send private email bon vivant 
April 5th, 2007 6:31pm
um, perl on windows.

I guess my computer is slow. shrug. if it only took two minutes, why didn't you go to lunch and see what happens when it hits 1000000?
Permalink Send private email strawberry snowflake 
April 5th, 2007 6:35pm
It was already after lunch and I didn't want it eating up all my CPU in the background. It was getting quite a bit slower at 30000 and not finding anything so I decided to stop there. I might write a C version and run it for longer this evening just for kicks.
Permalink Send private email bon vivant 
April 5th, 2007 6:49pm
yeah, the first 10,000 were quick. I set it to try 10,000 to 100,000 and left. I was pretty sure there was going to be another one.
Permalink Send private email strawberry snowflake 
April 5th, 2007 6:54pm
And to think, some people use their spare CPU cycles to find a cure for cancer or search for extra terrestrial life.
Permalink Send private email Сергей РахманиноB 
April 5th, 2007 7:00pm
This is probably more useful.
Permalink Send private email Ward 
April 5th, 2007 7:10pm
Even though it's a Repost Dildo...
Permalink Send private email Ward 
April 5th, 2007 7:10pm
Oh I know. My basic perl can't do numbers above 2^1023 ...

$ perl -e 'print 2**1023, "\n";'
8.98846567431158e+307
$ perl -e 'print 2**1024, "\n";'
inf

So I used Math::BigInt, which is slow.
Permalink Send private email strawberry snowflake 
April 5th, 2007 7:32pm
OK, so I searched all the way up to 2^1122938 and found no more. That's a number with about 400,000 digits in base 7 so it looks increasingly unlikely that another number will turn up. The probability that a number with that many digits will not have three consecutive digits the same must be vanishingly small.
Permalink Send private email bon vivant 
April 6th, 2007 1:43am
vivant, did you use Math::BigInt as well or did you take another approach?

I just wrote a script for bc. It sounds like perl's libraries are much faster.
Permalink Practical Economist 
April 6th, 2007 2:17am
No, I didn't consider using Math::BigInt at all, I didn't see that it was useful.

The first program I wrote was just a few lines of Perl, but Perl isn't too efficient for such low level calculations--it was slowing down somewhat at 2^30000. This evening I wrote a slightly more efficient version in C. It searches all the way up to 2^30000 in about 4 seconds, but it took more like 40 minutes to search up to 2^1000000.
Permalink Send private email bon vivant 
April 6th, 2007 3:05am
I just did 2^(30 million) in 47 minutes. I thought my original python program was pretty good (it took about 20 minutes to search from 50000 to 60000) til I read bon vivant's comment above. So I hacked up a C version and added the optimisation of only generating the least significant 8000 base 7 digits to look for triple zeros.
Permalink Send private email setsquare 
April 8th, 2007 10:29pm

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