%I A114830
%S A114830 1,2,4,6,9,13,18,24,31,39,48,59,71,85,101,119,139,162,187,215,246,280,
%T A114830 318,359,404
%N A114830 Each term is previous term plus ceiling of geometric mean of all previous 
               terms.
%C A114830 What is this sequence, asymptotically? a(n) is prime for n = 2, 6, 9, 
               12, 13, 15, 17, 24, ... are there an infinite number of prime values?
%H A114830 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GeometricMean.html">Geometric Mean.</a>
%F A114830 a(1) = 1, a(n+1) = a(n) + ceiling(GeometricMean[a(1),a(2),...,a(n)]). 
               a(n+1) = a(n) + ceiling[((a(1)*a(2)*,...,*a(n))^(1/n)].
%e A114830 a(2) = 1 + ceiling(1^(1/1)) = 1 + 1 = 2.
%e A114830 a(3) = 2 + ceiling[(1*2)^(1/2)] = 2 + ceiling[sqrt(2)] = 2 + 2 = 4.
%e A114830 a(4) = 4 + ceiling[(1*2*4)^(1/3)] = 4 + ceiling[CubeRoot(8)] = 4 + 2 
               = 6.
%e A114830 a(5) = 6 + ceiling[(1*2*4*6)^(1/4)] = 6 + floor[4thRoot(48)] = 6 + 3 
               = 9.
%e A114830 a(6) = 9 + ceiling[(1*2*4*6*9)^(1/5)] = 9 + ceiling[5thRoot(432)] = 9 
               + 4 = 13.
%e A114830 a(7) = 13 + ceiling[(1*2*4*6*9*13)^(1/6)] = 6 + floor[6thRoot(5616)] 
               = 13 + 5 = 18.
%e A114830 a(25) = 359 + ceiling[(1 * 2 * 4 * 6 * 9 * 13 * 18 * 24 * 31 * 39 * 48 
               * 59 * 71 * 85 * 101 * 119 * 139 * 162 * 187 * 215 * 246 * 280 * 
               318 * 359)^(1/24)] = 359 + ceiling[44.8074289] = 359 + 45 = 404.
%Y A114830 Cf. A065094, A065095.
%Y A114830 Sequence in context: A154255 A006697 A079717 this_sequence A001304 A000064 
               A001305
%Y A114830 Adjacent sequences: A114827 A114828 A114829 this_sequence A114831 A114832 
               A114833
%K A114830 easy,nonn
%O A114830 1,2
%A A114830 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006