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A268058
Maximum value of n-th row of A268057.
5
1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 5, 3, 4, 4, 3, 3, 5, 4, 6, 4, 4, 5, 6, 3, 5, 4, 5, 4, 5, 4, 6, 4, 5, 6, 7, 4, 5, 6, 5, 4, 6, 4, 6, 5, 5, 7, 8, 4, 7, 5, 6, 5, 9, 5, 6, 5, 6, 6, 8, 4, 7, 6, 6, 5, 7, 5, 8, 7, 7, 7, 6, 4, 6, 6, 5, 7, 7, 6, 8, 5, 5, 6, 9, 5, 6, 6, 7
OFFSET
1,3
LINKS
Zachary Chase and Mayank Pandey, On the length of Pierce expansions, arXiv preprint (2022). arXiv:2211.08374 [math.NT]
P. Erdős and J. O. Shallit, New bounds on the length of finite Pierce and Engel series, Journal de Théorie des Nombres de Bordeaux 3:1 (1991), pp. 43-53.
J. O. Shallit, Metric theory of Pierce expansions, Fibonacci Quart. 24 (1986), pp. 22-40.
Reddit user zifyoip, First 100 terms.
FORMULA
Chase & Pandey prove that a(n) = O(n^e) for any e > 19/59 = 0.322..., improving on Kešelj, Erdős & Shallit, and Shallit. - Charles R Greathouse IV, Jan 13 2023
PROG
(PARI) P(a, b)=my(n); while(b, b=a%b; n++); n
a(n)=my(t=1); for(b=2, n-1, t=max(P(n, b), t)); t \\ Charles R Greathouse IV, Nov 26 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Jan 25 2016
STATUS
approved