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 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..50. Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, Convergence Acceleration of Alternating Series, Experimental Mathematics, 9:1 (2000). Eric Weisstein's World of Mathematics, MRB Constant. Wikipedia, Mathematical constant 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 Cf. A037077 (the MRB constant). Sequence in context: A228881 A252373 A245338 * A017873 A274016 A291572 Adjacent sequences: A160752 A160753 A160754 * A160756 A160757 A160758 KEYWORD nonn,base,less AUTHOR Marvin Ray Burns, May 25 2009 EXTENSIONS Corrections from Marvin Ray Burns, Jun 05 2009 Link to Wikipedia replaced by up-to-date version; keyword:less added R. J. Mathar, Aug 04 2010 Corrections by Marvin Ray Burns, Aug 21 2010, Jul 15 2012 STATUS approved

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Last modified August 13 11:45 EDT 2024. Contains 375138 sequences. (Running on oeis4.)