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19h
revised Do runs of every length occur in this string?
update with search results for c^7
1d
awarded  Nice Question
1d
comment Do runs of every length occur in this string?
Oops, that was a typo on my part (now fixed): the index for $\text{c}^6$ is actually $\approx 2.124\ 10^{519}$ (a $520$-digit number!). Of course, that program is doing a smarter search, and the number of positions it has to check is only a very very tiny fraction of $10^{519}$.
1d
revised Do runs of every length occur in this string?
fix typos
2d
comment Do runs of every length occur in this string?
@Calvin'sHobbies - Thanks for the link -- the program posted there succeeded in finding the first occurrence of $\text{c}^6$! (I edited it into the table above.)
2d
revised Do runs of every length occur in this string?
update the first-occurrence index for c^6, which is now known
Jul
26
revised Do runs of every length occur in this string?
prove or disprove
Jul
26
comment Do runs of every length occur in this string?
By switching to a system with more memory (again using Sage), I was able to extend the search to $55$ rewrites, with the result that $\text{c}^6$ does not occur in the first $17,673,600,662$ ($17^+$ billion) terms of $s$. I've updated the table.
Jul
26
revised Do runs of every length occur in this string?
update the search result for c^6
Jul
25
comment Do runs of every length occur in this string?
Your program does not prove that ($\forall k, \text{c}^k \text{ occurs in }s$), because it must be used to test every $k=1,2,3,...$ (infinitely many) -- a procedure that never halts. (Of course I used a similar program to compute the short table of first-occurrence indices posted in the question. On my system, using Sage, 47 rewrites was the maximum without memory errors.)
Jul
25
comment Does this sequence have any mathematical significance?
I've posted a "spin-off" question: Do runs of every length occur in this string?.
Jul
25
revised Do runs of every length occur in this string?
extended search results for c^6
Jul
24
comment Do runs of every length occur in this string?
@Sid -- I would be interested in any algorithm/program capable of proving the conjecture. (I'm skeptical that any such is available, however.)
Jul
24
comment Do runs of every length occur in this string?
@Semiclassical -- The initial $\text{a}$ just acts as a "placeholder". The same sequence (without the initial $\text{a}$) is generated by starting with $\text{bc}$ and using the modified rewriting rule $a_1 \cdots a_{n} \ \ \to \ \ a_1 \cdots a_{n} a_{\left\lfloor\frac{n+1}{2}\right\rfloor } a_{\left\lfloor\frac{n+1}{2}\right\rfloor+1} \cdots a_{n}$, but I don't see how this helps. (BTW, your reference to "my" previous question suggests that you've mistaken me for the poster of the linked question.)
Jul
24
asked Do runs of every length occur in this string?
Jul
16
revised Finding a specific sequence of digits in pi
Precise definition of first-occurrence time; indexing starts at 1 (not 0).
Jul
14
revised Finding a specific sequence of digits in pi
improve wording
Jul
14
revised Finding a specific sequence of digits in pi
add tag [probability], remove [infinite-groups]
Jul
14
suggested suggested edit on Finding a specific sequence of digits in pi
Jul
13
revised Finding a specific sequence of digits in pi
added 4 characters in body