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A301275
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Numerator of variance of first n primes.
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6
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0, 1, 7, 59, 64, 581, 649, 2287, 1001, 2443, 5669, 17915, 6665, 36637, 3529, 22413, 22813, 13065, 75865, 191819, 58778, 289013, 7627, 141973, 5213, 628001, 370333, 96211, 249436, 381167, 672727, 1565639, 453767, 691587, 1194917, 301867, 770294
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OFFSET
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1,3
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COMMENTS
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Variance here is the sample variance unbiased estimator. - Chai Wah Wu, Mar 22 2018
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LINKS
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EXAMPLE
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The variances are 0, 1/2, 7/3, 59/12, 64/5, 581/30, 649/21, 2287/56, 1001/18, 2443/30, 5669/55, 17915/132, 6665/39, 36637/182, 3529/15, 22413/80, 22813/68, 13065/34, 75865/171, 191819/380, 58778/105, 289013/462, 7627/11, 141973/184, 5213/6, 628001/650, ...
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MAPLE
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v := n -> 1/(n-1) * add((ithprime(i) add(ithprime(j), j=1..n)/n)^2, i=1..n );
v1:= [0, seq(v(n), n=2..70)];
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MATHEMATICA
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a[n_] := If[n == 1, 0, Variance[Prime[Range[n]]] // Numerator];
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PROG
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(Python)
from fractions import Fraction
from sympy import prime
mu, variance = Fraction(prime(1)), Fraction(0)
A301275_list = [variance.numerator]
for i in range(2, 10001):
datapoint = prime(i)
newmu = mu+(datapoint-mu)/i
variance = (variance*(i-2) + (datapoint-mu)*(datapoint-newmu))/(i-1)
mu = newmu
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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