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 A224365 #58 Jul 13 2021 19:47:19 %S A224365 10,3,3,3,157,22,22,22,22,22,22,22,22,51808,355,355,355,355,355,355, %T A224365 355,355,355,355,355,355,355,355,355,355,355,355,355,355,355,355,355, %U A224365 355,355,355,355,355,355,355,355,355,355,355 %N A224365 a(n) = A063674(n+1) - A063674(n). %C A224365 The repeated terms (3, 22, 355, 5419351, ... from A063674) are the numerators of fractions (3/1, 22/7, 355/113, 5419351/1725033, ...) leading to Pi. %C A224365 Zu Chongzhi (5th century) discovered 22/7 and 355/113. Adriaan Anthonisz Metius rediscovered 355/113 in 1585. %C A224365 First differences of A063673 give the denominators: 3, 1, 1, 1, 50, 7, 7, 7, 7, 7, 7, 7, 7, 16489, 113, 113, ... . %C A224365 Hence 10/3, 157/50, 51808/16489, ... . %H A224365 Vincenzo Librandi, <a href="/A224365/b224365.txt">Table of n, a(n) for n = 1..168</a> %F A224365 a(n) = A063674(n+1) - A063674(n). %t A224365 A224365 = Reap[ For[ delta0 = 1; d = 1, d < 10^5, d++, delta = Abs[Pi - Round[Pi*d]/d]; If[ delta < delta0, Sow[ Round[Pi*d]]; delta0 = delta]]][[2, 1]] // Differences (* _Jean-François Alcover_, Apr 10 2013 *) %Y A224365 Cf. A063673, A063674. %Y A224365 Cf. A046947, A072398, A002485. A132049, A003077, A068028, A068079. %K A224365 nonn,less,frac %O A224365 1,1 %A A224365 _Paul Curtz_, Apr 09 2013