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 A164086 #15 Feb 16 2025 08:33:11 %S A164086 4,8,12,16,20,25,29,33,37,41,46,50,54,58,62,67,71,75,79,83,87,92,96, %T A164086 100,104,108,113,117,121,125,129,134,138,142,146,150,154,159,163,167, %U A164086 171,175,180,184,188,192,196,201,205,209,213,217,222,226,230,234,238,242 %N A164086 Beatty sequence for 4*Pi/3 = 4.1887902... . %C A164086 a(n) = A109238(n) for n <= 20; %C A164086 complement of A164087; %C A164086 a(n) = A164088(A164087(n)) and A164088(a(n)) = A164087(n); %C A164086 a(A000578(n)) = A066645(n). %H A164086 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a> %H A164086 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a> %F A164086 a(n) = floor(4*n*Pi/3). %e A164086 a(3^3) = a(27) = 113 = (integer part of volume of sphere with radius=3) = A066645(3). %t A164086 With[{c=4 \[Pi]/3},Floor[c #]&/@Range[70]] (* _Harvey P. Dale_, Mar 19 2011 *) %o A164086 (Maxima) %o A164086 fprec:100$ %o A164086 A164086:4*%pi/3$ %o A164086 ev(bfloat(A164086)); /* _Martin Ettl_, Nov 03 2012 */ %Y A164086 Cf. A022844, A019699. %K A164086 nonn %O A164086 1,1 %A A164086 _Reinhard Zumkeller_, Aug 11 2009