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A114830 Each term is previous term plus ceiling of geometric mean of all previous terms. 1
1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 48, 59, 71, 85, 101, 119, 139, 162, 187, 215, 246, 280, 318, 359, 404, 453, 507, 565, 628, 697, 771, 851, 937, 1029, 1128, 1234, 1348, 1470, 1600, 1738, 1885, 2042, 2209, 2386, 2574, 2773, 2984, 3207, 3443, 3692, 3955, 4232, 4524, 4831, 5154, 5494, 5851, 6226, 6620 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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?

LINKS

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Geometric Mean.

FORMULA

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)].

EXAMPLE

a(2) = 1 + ceiling(1^(1/1)) = 1 + 1 = 2.

a(3) = 2 + ceiling[(1*2)^(1/2)] = 2 + ceiling[sqrt(2)] = 2 + 2 = 4.

a(4) = 4 + ceiling[(1*2*4)^(1/3)] = 4 + ceiling[CubeRoot(8)] = 4 + 2 = 6.

a(5) = 6 + ceiling[(1*2*4*6)^(1/4)] = 6 + floor[4thRoot(48)] = 6 + 3 = 9.

a(6) = 9 + ceiling[(1*2*4*6*9)^(1/5)] = 9 + ceiling[5thRoot(432)] = 9 + 4 = 13.

a(7) = 13 + ceiling[(1*2*4*6*9*13)^(1/6)] = 6 + floor[6thRoot(5616)] = 13 + 5 = 18.

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.

MAPLE

A114830 := proc(n)

    option remember;

    if n= 1 then

        1;

    else

        mul(procname(i), i=1..n-1) ;

        procname(n-1)+ceil(root[n-1](%)) ;

    end if;

end proc:

seq(A114830(n), n=1..60) ; # R. J. Mathar, Jun 23 2014

CROSSREFS

Cf. A065094, A065095.

Sequence in context: A247179 A319158 A175780 * A177239 A001304 A000064

Adjacent sequences:  A114827 A114828 A114829 * A114831 A114832 A114833

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 19 2006

STATUS

approved

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Last modified November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)