A341052 - OEIS

%I #26 May 02 2021 11:03:49

%S 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,

%T 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,

%U 1,3,2,3,2,1,3,1,2,4,2,4,3,1,3,3,3,2,1

%N 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.

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

%C 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).

%C The numerators of corresponding ratios are in A341053.

%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/2006-a10219-progressions-maximales">A10219, Progressions maximales</a> (in French).

%e 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.

%e From _Jinyuan Wang_, Apr 18 2021: (Start)

%e 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:

%e -> with ratio = 4/3, the 8 integers go from 10935 to 81920,

%e -> with ratio = 5/4, the 8 integers go from 16384 to 78125.

%e so a(5) = 2. (End)

%Y Cf. A341051, A341053.

%K nonn,base

%O 1,5

%A _Bernard Schott_, Apr 16 2021

%E a(5) corrected by and more terms from _Jinyuan Wang_, Apr 18 2021