OFFSET
1,2
COMMENTS
If we let L(n) denote the number of digits in the n-th term, then the limit of L(n+1)/L(n) is an algebraic integer of degree 415. This limit is a stuttering analog of Conway's constant (see A014715).
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..18
Jonathan Comes, Stuttering look and say sequences and a challenger to Conway's most complicated algebraic number from the silliest source, arXiv:2206.11991 [math.HO], 2022.
EXAMPLE
E.g., to obtain the term after 1110, we look at 1110 and see "three 1's and one 0". We then say what we saw by stuttering the counts as many times as the count prescribes: we stutter the "three" 3 times and the "one" 1 time (no stutter); so we say "three three three 1's and one 0" to get 333110.
PROG
(Python)
from itertools import accumulate, groupby, repeat
def summarize(n, _): return int("".join(str(c:=len(list(g)))*c+k for k, g in groupby(str(n))))
def aupton(terms): return list(accumulate(repeat(0, terms), summarize))
print(aupton(11)) # Michael S. Branicky, Jun 28 2022
(PARI) first(n) = my(c, d=[0], x, res=vector(n)); for(i=2, n, c=1; x=""; for(j=1, #d, if(j<#d && d[j]==d[j+1], c++, x=concat(x, concat(vector(c+1, k, Str(if(k==c+1, d[j], c))))); c=1)); res[i]=eval(x); d=digits(res[i])); res \\ Iain Fox, Jun 30 2022
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Jonathan Comes, Jun 28 2022
STATUS
approved