I think I just discovered supernormalcy

by super_normalon 12/21/2024, 7:33 PMwith 7 comments

the first 1,000 digits of 17^(1/7) after the ones form (not verified) a perfect de bruijn sequence. no other irrational number i have tried comes close. possibly applicable to number theory et al. any mathematicians here care to verify or comment? etcetera.

(opps. it looks like claude was hallucinating. i was trusting it to detect this feature and not hallucinate. my bad for trusting.)

((just looking at the sequence, the digit '7' seems to have non trivial occurance patterns. can anyone maybe try some statistical analysis on the regularity of this to save this thread posting etc?))

(((etcetera.)))

by jepleron 12/21/2024, 8:04 PM

assuming you mean the decimal expansion and a length-3 de bruijn sequence on 10 symbols, I am not seeing it. There seem to be many sub-sequences which do not appear. (assuming that python's Decimal library at a precision of 4000 digits is actually giving the first 1000 digits correctly; though I have no reason to doubt this I don't know for sure the maximum ULP error of exponent)

    Python 3.11.2 (main, Sep 14 2024, 03:00:30) [GCC 12.2.0] on linux
    Type "help", "copyright", "credits" or "license" for more information.
    >>> from decimal import Decimal, getcontext
    >>> getcontext().prec = 4000
    >>> d = 17 ** (1 / Decimal(7))
    >>> sd = str(d)
    >>> sd[:12]
    '1.4989198720'
    >>> s = sd[2:][:1000]
    >>> s[:10], s[-10:]
    ('4989198720', '6163659068')
    >>> [i for i in range(1000) if "%03d" % i not in s+s]
    [0, 2, 4, 5, 9, [...], 993, 994, 995, 998, 999]
    >>> len(_)
    361

by pavel_lishinon 12/21/2024, 7:46 PM

> a perfect de bruijn sequence

My understanding is that this means that every possible substring appears at least once, right? But what does this mean for the first thousand digits? Does that mean that every two-digit sequence appears at least once, three digit sequence, etc?

by super_normalon 12/21/2024, 8:55 PM

my bad. claude 3.5 sonnet was lying to me. i tried to get it to check itself and it gave me back nonsense 3 times in a row. i just decided to check this property on irrationals and he hallucinated that the counts were more even than the facts are. always double check claude outputs. it still wont even write the real code properly. sorry guys. etc. ...