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 A173273 Decimal expansion of  M2 = 1 - 2*M where M is the MRB constant A037077. 1
 6, 2, 4, 2, 8, 0, 7, 1, 5, 0, 7, 5, 8, 6, 5, 7, 5, 9, 5, 0, 2, 9, 6, 4, 1, 3, 1, 8, 9, 1, 4, 5, 3, 5, 3, 9, 8, 8, 8, 1, 9, 3, 8, 1, 0, 1, 9, 9, 7, 2, 2, 4, 2, 7, 6, 5, 5, 9, 9, 0, 6, 3, 1, 8, 2, 1, 0, 4, 5, 5, 3, 6, 8, 7, 0, 6, 7, 9, 5, 7, 2, 5, 9, 3, 4, 0, 6, 6, 9, 1, 1, 3, 3, 7, 8, 5, 0, 0, 6, 1, 9, 2, 3, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Below regularization is used so that the sum that formally diverges returns a result that can be interpreted as evaluation of the analytic extension of the series: For any number b, let S=sum((-1)^k (k^(1/k)-b), k=1..infinity) = 1/2*(b+2M-1) then b=2S+M2. Obviously, when b = M2 then S = 0, so sum((-1)^k*(k^(1/k)-M2), k=1..infinity) = 0 and limit(sum((-1)^m*(m^(1/m)-M2), m =1..2*N), N= infinity) = M = limit(sum((-1)^m*(M2-m^(1/m)), m=1..2*N-1), N=infinity). LINKS Leonhard Paul Euler, Likewise, Euler shows that the sum of the divergent series 1-2+3-4+5 + etc. is 1/4. Marvin Ray Burns, Author's original inquiry Wolfram Alpha, 1-2*MRB constant EXAMPLE 1-2*MRB constant = 0.624280715... MATHEMATICA digits = 105; 1-2*NSum[ (-1)^n*((n^(1/n)) - 1), {n, 1, Infinity}, WorkingPrecision -> digits+10, Method -> "AlternatingSigns"] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013 *) CROSSREFS Cf. A037077. Sequence in context: A198502 A244858 A064925 * A084945 A010493 A175286 Adjacent sequences:  A173270 A173271 A173272 * A173274 A173275 A173276 KEYWORD nonn,cons AUTHOR Marvin Ray Burns, Feb 14 2010, Feb 24 2010, Mar 05 2010 EXTENSIONS Edited by Marvin Ray Burns, Apr 15 2010, Mar 04 2013 STATUS approved

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)
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