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A114829
Each term is previous term plus floor of geometric mean of all previous terms.
2
1, 2, 3, 4, 6, 8, 11, 14, 18, 23, 29, 36, 44, 53, 63, 74, 87, 101, 117, 135, 155, 177, 201, 227, 256, 287, 321, 358, 398, 442, 489, 540, 595, 654, 717, 785, 858, 936, 1019, 1107, 1201, 1301, 1408, 1521, 1641, 1768, 1903, 2046, 2197, 2356, 2524, 2701, 2888, 3085, 3292, 3510, 3739, 3979, 4231
OFFSET
1,2
COMMENTS
What is this sequence, asymptotically?
LINKS
Eric Weisstein's World of Mathematics, Geometric Mean.
FORMULA
a(1) = 1, a(n+1) = a(n) + floor(GeometricMean[a(1),a(2),...,a(n)]).
a(n+1) = a(n) + floor((Product_{k=1..n} a(k))^(1/n)).
EXAMPLE
a(2) = 1 + floor(1^(1/1)) = 1 + 1 = 2.
a(3) = 2 + floor[(1*2)^(1/2)] = 2 + floor[sqrt(2)] = 2 + 1 = 3.
a(4) = 3 + floor[(1*2*3)^(1/3)] = 3 + floor[CubeRoot(6)] = 3 + 1 = 4.
a(5) = 4 + floor[(1*2*3*4)^(1/4)] = 4 + floor[4thRoot(24)] = 4 + 2 = 6.
a(6) = 6 + floor[(1*2*3*4*6)^(1/5)] = 6 + floor[5thRoot(144)] = 6 + 2 = 8.
a(7) = 8 + floor[(1*2*3*4*6*8)^(1/6)] = 6 + floor[6thRoot(1152)] = 8 + 3 = 11.
MAPLE
A114829 := proc(n)
option remember;
if n= 1 then
1;
else
mul(procname(i), i=1..n-1) ;
procname(n-1)+floor(root[n-1](%)) ;
end if;
end proc:
seq(A114829(n), n=1..60) ; # R. J. Mathar, Jun 23 2014
MATHEMATICA
s={1}; Do[AppendTo[s, Last[s]+Floor[GeometricMean[s]]], {n, 58}]; s (* James C. McMahon, Aug 19 2024 *)
CROSSREFS
Sequence in context: A238383 A134953 A175870 * A175869 A007279 A034891
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 19 2006
STATUS
approved