A341052 a(n) is the number of distinct ratios > 1 for which there exist A341051(n) n-digit integers (the maximum possible) that are in geometric progression.

1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 3, 1, 3, 3, 1, 1, 3, 1, 2, 2, 3, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 2, 1, 1, 1, 3, 1, 4, 2, 3, 3, 1, 3, 2, 3, 2, 1, 3, 1, 2, 4, 2, 4, 3, 1, 3, 3, 3, 2, 1

Offset

1,5

Comments

The ratios are of the form m/(m-1) with m > 1.

The first few successive ratios are 2, 3/2, 3/2, 4/3, then a(5) = 2 because the two ratios 4/3 and 5/4 both give the largest possible number A341051(5) = 8 of 5-digit integers that are in geometric progression (see examples).

The numerators of corresponding ratios are in A341053.

Links

Table of n, a(n) for n=1..87.

Diophante, A10219, Progressions maximales (in French).

Example

There exist 6 integers in the largest possible string with 3-digit numbers that are in geometric progression (128, 192, 288, 432, 648, 972), and this string is obtained with the ratio = 3/2, so a(3) = 1.
From Jinyuan Wang, Apr 18 2021: (Start)
There exist 8 integers in the largest possible string with 5-digit numbers that are in geometric progression, and two such strings are obtained with these 2 distinct following ratios:
-> with ratio = 4/3, the 8 integers go from 10935 to 81920,
-> with ratio = 5/4, the 8 integers go from 16384 to 78125.
so a(5) = 2. (End)

Crossrefs

Cf. A341051, A341053.

Sequence in context: A079115 A072906 A239062 * A201160 A302538 A228428

Adjacent sequences: A341049 A341050 A341051 * A341053 A341054 A341055

Keyword

nonn,base

Author

Bernard Schott, Apr 16 2021

Extensions

a(5) corrected by and more terms from Jinyuan Wang, Apr 18 2021

Status

approved