

A160755


Number of correct digits of the MRB constant derived from the sequence of partial sums up to m=10^n terms as defined by S[n]= Sum[(1)^k*(k^(1/k)1),{k,m}].


1



1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49
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OFFSET

1,2


COMMENTS

Adding the series 1+sqrt(2)3^(1/3)+4^(1/4)..., according to this sequence, 10 billion terms must be added to arrive at 11 accurate digits of the MRB constant.


REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 450. ISBN 0521818052.


LINKS



EXAMPLE

For n=1, a(n)=1 because after 10^1 partial sums of 1+sqrt(2)3^(1/3)+4^(1/4)... you get one accurate digit of the MRB constant.
For n=2, a(n)=2 because after 10^2 partial sums you get two accurate digits and so on.


MATHEMATICA

m = NSum[(1)^n*(n^(1/n)  1), {n, Infinity}, Method > "AlternatingSigns", WorkingPrecision > 1000]; Table[Floor[Log[10, Abs[m  NSum[(1)^n*(n^(1/n)  1), {n, 10^a}, Method >"AlternatingSigns", WorkingPrecision > 1000]]]], {a, 1, 50}]


CROSSREFS



KEYWORD

nonn,base,less


AUTHOR



EXTENSIONS

Link to Wikipedia replaced by uptodate version; keyword:less added R. J. Mathar, Aug 04 2010


STATUS

approved



