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A082912 Sum of a(n) terms of harmonic series Sum 1/i is > 10^n. 1
2, 12367, 15092688622113788323693563264538101449859497 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

"In 1968 John W. Wrench Jr calculated the exact minimum number of terms needed for the series to sum past 100; that number is 15 092 688 622 113 788 323 693 563 264 538 101 449 859 497. Certainly, he did not add up the terms.

"Imagine a computer doing so and suppose that it takes it 10^-9 seconds to add each new term to the sum and that we set it adding and let it continue doing so indefinitely. The job will have heen completed in not less than 3.5 * 10^17 (American) billion years." Havil.

REFERENCES

R. Baillie, Fun With Very Large Numbers, Arxiv preprint arXiv:1105.3943, 2011

Boas, R. P. and Wrench, J. W. "Partial Sums of the Harmonic Series." Amer. Math. Monthly 78, 864-870, 1971.

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 23.

Lin Zhang, A Likelihood Ratio Test of Independence of Components for High-dimensional Normal Vectors, MS Thesis, Univ. Minnesota, 2013; http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202013/Lin%20Zhang%20thesis_masters-4.pdf

LINKS

Table of n, a(n) for n=0..2.

Eric Weisstein's World of Mathematics, Harmonic Number

FORMULA

H_n ~= Ln(n) + Euler's Gamma Constant (A001620) + 1/(2n).

MATHEMATICA

f[n_] := Floor[Exp[n - EulerGamma] - 1/2] + 1; Table[ f[10^n], {n, 0, 2}]

CROSSREFS

Cf. A002387, A001620.

Sequence in context: A134656 A128122 A082178 * A083973 A094212 A070832

Adjacent sequences:  A082909 A082910 A082911 * A082913 A082914 A082915

KEYWORD

nonn,bref

AUTHOR

Robert G. Wilson v, Apr 14 2003

STATUS

approved

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Last modified July 30 09:31 EDT 2014. Contains 245062 sequences.