A268058 Maximum value of n-th row of A268057.

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

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.

Index entries for sequences related to Engel expansions

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

Cf. A268057, A268059, A268060.

Sequence in context: A179844 A076223 A076235 * A334686 A057941 A358550

Adjacent sequences: A268055 A268056 A268057 * A268059 A268060 A268061

Keyword

nonn

Author

Peter Kagey, Jan 25 2016

Status

approved