I think I just discovered supernormalcy

[super_normal]

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.)))

[jepler]

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

[super_normal]

id prefer it if you would write this in haskell so i can understand what is going on there better. i am saying of the first 1,000 digits after the ones place, each digit of the sequence appears an even number of times, every consecutive subsequence of two appears an even number of times, and every consecutive subsequence of three happens exactly once. please, if you could do some more intelligable work and show your result as standard deviations away from the the exact de bruijn counts i would really appreciate it. etcetcera.

(i dont know where you got the 10 symbols from. im talking about over the entire 1,000 length decimal sequence. etcetera.)

[pavel_lishin]

> 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?

[super_normal]

yes. and i think this is perfect up to three. no other number i tested was anywhere close to this, and i suspect it may lead to an important new metric. please verify.

(and i should add i think it also means that all the counts are completely even for one and two.)

[super_normal]

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. ...