[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.)

[jepler]

I don't know Haskell, so I can imagine if you didn't know Python it'd be "greek to you" (unintelligible). I'll try explaining in prose what I did. [note: I also edited the grandparent comment because when I simplified the session I showed, the assignment of "s" ended up out of order]

I use the Python decimal package to calculate 17^(1/7) to 4000 decimal places. I show the first 12 characters of the ASCII representation ("1.4989198720"), then take the first 1000 characters after the decimal place. I show the first and last 10 characters of this string ("4989198720...6163659068") so that you can verify it against the string you are testing.

Then I use a list comprehension to check each 3-digit string (e.g., 001, 002, 003, ..., 999) to find out whether it is a substring of the concatenation of `s` with itself, and list the ones that don't appear. I manually abbreviated the list, but I'm saying that in my string, 000, 002, 004, 005, 009, [and some other numbers], 993, 994, 995, 998, and 999 did not appear. (The concatenation `s+s` is checked so that the subsequences that occur at the wraparound---here,684 and 849---are found)

Because some of these length-3 sequences are missing, to my understanding this does not constitute a de Bruijn sequence of order 3 on a size-10 alphabet. However, I'm also not entirely sure whether this is what you were claiming.