OFFSET
1,3
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10000
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.
Vlado Kešelj, Length of finite Pierce series: theoretical analysis and numerical calculations (1996), 27 pp.
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