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A355316
Stuttering Look and Say sequence with seed 0.
1
0, 10, 1110, 333110, 333322110, 4444322222110, 444441355555222110, 5555541113555555333222110, 5555551433311366666653333333222110, 6666665111433332211366666661577777773333222110, 66666661533311444443222221137777777611157777777744443333222110
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).
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
Stuttering variant of A001155.
Cf. A014715.
Sequence in context: A001391 A049064 A267246 * A266589 A015026 A130598
KEYWORD
base,nonn
AUTHOR
Jonathan Comes, Jun 28 2022
STATUS
approved