This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138374 #14 Mar 29 2020 17:13:19 %S A138374 1,1,2,2,3,4,4,6,6,8,6,10,10,12,13,15,16,17,16,18,19,20,21,21,22,23, %T A138374 25,27,28,29,30,31,32,35,38,39,40,39,41,42,45,46,46,47,49,51,52,52,54, %U A138374 56,56,57,58,58,60,61,62,63,65,64,66,68,69,69,70,70,72,74,74,75,77,79,81 %N A138374 Count of post-period decimal digits up to which the rounded n-th convergent to 2^(1/3) agrees with the exact value. %C A138374 This is a measure of the quality of the n-th convergent to the constant A002580 if the convergent and the exact value are compared rounded to an increasing number of digits. The sequence of rounded values of A002580 is 1, 1.3, 1.26, 1.260, 1.2599, 1.25992, 1.259921, 1.2599211 etc. The n-th convergents are taken from A002352 and A002351, each with associated rounded decimal expansions. %C A138374 a(n) is the maximum number of post-period digits of the two expansions if compared at the same level of rounding. %e A138374 For n=5, the 5th convergent is 63/50 = 1.26000000.., with a sequence of rounded representations 1, 1.3, 1.26, 1.260, 1.2600, 1.26000, etc. %e A138374 Rounded to 1, 2, or 3 post-period decimal digits, this is the same as the rounded version of the exact value, but disagrees if both are rounded to 4 decimal digits, where 1.2599 <> 1.2600. %e A138374 So a(5) = 3 (digits), the maximum rounding level with agreement. %Y A138374 Cf. A138335 - A138339, A138343, A138366, A138367, A138369 - A138373. %K A138374 base,nonn %O A138374 1,3 %A A138374 _Artur Jasinski_, Mar 17 2008 %E A138374 Definition and values replaced as defined via continued fractions - _R. J. Mathar_, Oct 01 2009