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 A199493 #18 Jul 23 2025 22:54:30 %S A199493 3,17,129,1025,8193,65537,524289,4194305,33554433,268435457, %T A199493 2147483649,17179869185,137438953473,1099511627777,8796093022209, %U A199493 70368744177665,562949953421313,4503599627370497,36028797018963969 %N A199493 a(n) = 2*8^n+1. %C A199493 An Engel expansion of 4 to the base 8 as defined in A181565, with the associated series expansion 4 = 8/3 + 8^2/(3*17) + 8^3/(3*17*129) + 8^4/(3*17*129*1025) + .... Cf. A087289 and A199552. - _Peter Bala_, Oct 30 2013 %H A199493 Vincenzo Librandi, <a href="/A199493/b199493.txt">Table of n, a(n) for n = 0..1000</a> %H A199493 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8). %F A199493 a(n) = 8*a(n-1)-7. %F A199493 a(n) = 9*a(n-1)-8*a(n-2). %F A199493 G.f.: (3-10*x)/((1-x)*(1-8*x)). %t A199493 2*8^Range[0, 20] + 1 (* _Wesley Ivan Hurt_, Jul 23 2025 *) %o A199493 (Magma) [2*8^n+1: n in [0..30]]; %Y A199493 Cf. A087289, A181565, A199552. %K A199493 nonn,easy %O A199493 0,1 %A A199493 _Vincenzo Librandi_, Nov 07 2011