OFFSET
1,3
COMMENTS
In the definition (and example), multiplication denotes concatenation of words. This is similar to Gijswijt's sequence A090822 except that we accept blocks as being equivalent if they are merely permutations of each other, not necessarily via the identity permutation (as is the case in A090822).
Question: Is it true that for all m, a(1)a(2)a(3)...a(m) above shows up somewhere in Gijswijt's sequence (A090822)?
LINKS
Samuel Harkness, Table of n, a(n) for n = 1..10000
Samuel Harkness, MATLAB program
Neal Gersh Tolunsky, Ordinal transform of the first 20000 terms
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
EXAMPLE
PROG
(MATLAB) See Links section.
(Python)
def k(s):
maxk = 1
for m in range(1, len(s)+1):
i, y, kk = 1, sorted(s[-m:]), len(s)//m
if kk <= maxk: return maxk
while sorted(s[-(i+1)*m:-i*m]) == y: i += 1
maxk = max(maxk, i)
def aupton(terms):
alst = [1]
for n in range(2, terms+1):
alst.append(k(alst))
return alst
print(aupton(105)) # Michael S. Branicky, Nov 05 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Taylor (integersfan(AT)yahoo.com), Mar 15 2004
STATUS
approved