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 A085613 #12 Apr 07 2024 07:13:43 %S A085613 2,3,5,11,17,41,65,155,257,593,1025,2291,4097,8921,16385,34955,65537, %T A085613 137633,262145,543971,1048577,2156201,4194305,8565755,16777217, %U A085613 34085873,67108865,135812051,268435457,541653881,1073741825,2161832555,4294967297,8632981313 %N A085613 a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2). %C A085613 Extends Euler's 6-term sequence. %C A085613 In Euler's 6-term sequence we have noticed that e(1) = 2 = 2^0 + 1; e(2) = 3 = 2^1 + 3^0; e(3) = 5 = 2^2 + 1; e(4) = 11 = 2^3 + 3^1; e(5) = 17 = 2^4 + 1; e(6) = 41 = 2^5 + 3^2, which of course immediately leads to our formula above. Note: For m>0, we take m^(1/2) to be the unique positive square root of m. %C A085613 a(2^n + 1), n=0,1,2,... are the Fermat numbers. %H A085613 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-8,-3,6). %o A085613 (PARI) a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2) \\ _Charles R Greathouse IV_, Jan 29 2013 %Y A085613 Cf. A082605. %K A085613 nonn,easy %O A085613 1,1 %A A085613 Ben de la Rosa & Johan Meyer (MeyerJH.sci(AT)mail.uovs.ac.za), Jul 09 2003 %E A085613 More terms from Neven Juric, Apr 10 2008