%I A114829
%S A114829 1,2,3,4,6,8,11,14,18,23,29,36,44,53,63,74,87,101,117,135,155,177,201,
%T A114829 227,256
%N A114829 Each term is previous term plus floor of geometric mean of all previous 
               terms.
%C A114829 What is this sequence, asymptotically? a(n) is prime for n = 2, 3, 7, 
               10, 11, 14, 18, 24, ... are there an infinite number of prime values?
%H A114829 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GeometricMean.html">Geometric Mean.</a>
%F A114829 a(1) = 1, a(n+1) = a(n) + floor(GeometricMean[a(1),a(2),...,a(n)]). a(n+1) 
               = a(n) + [((a(1)*a(2)*,...,*a(n))^(1/n)].
%e A114829 a(2) = 1 + floor(1^(1/1)) = 1 + 1 = 2.
%e A114829 a(3) = 2 + floor[(1*2)^(1/2)] = 2 + floor[sqrt(2)] = 2 + 1 = 3.
%e A114829 a(4) = 3 + floor[(1*2*3)^(1/3)] = 3 + floor[CubeRoot(6)] = 3 + 1 = 4.
%e A114829 a(5) = 4 + floor[(1*2*3*4)^(1/4)] = 4 + floor[4thRoot(24)] = 4 + 2 = 
               6.
%e A114829 a(6) = 6 + floor[(1*2*3*4*6)^(1/5)] = 6 + floor[5thRoot(144)] = 6 + 2 
               = 8.
%e A114829 a(7) = 8 + floor[(1*2*3*4*6*8)^(1/6)] = 6 + floor[6thRoot(1152)] = 8 
               + 3 = 11.
%Y A114829 Cf. A065094, A065095.
%Y A114829 Sequence in context: A059291 A075535 A134953 this_sequence A007279 A034891 
               A143611
%Y A114829 Adjacent sequences: A114826 A114827 A114828 this_sequence A114830 A114831 
               A114832
%K A114829 easy,nonn
%O A114829 1,2
%A A114829 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006