%I A085613
%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
%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.
%e A085613 a(2^n + 1), n=0,1,2,... are the Fermat numbers.
%Y A085613 Cf. A082605.
%Y A085613 Sequence in context: A014210 A014556 A062737 this_sequence A082605 A007755 
               A060611
%Y A085613 Adjacent sequences: A085610 A085611 A085612 this_sequence A085614 A085615 
               A085616
%K A085613 nonn
%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