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Search: id:A037077
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| A037077 |
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Decimal expansion of 1^(1/1)-2^(1/2)+3^(1/3)... |
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+0
4
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| 1, 8, 7, 8, 5, 9, 6, 4, 2, 4, 6, 2, 0, 6, 7, 1, 2, 0, 2, 4, 8, 5, 1, 7, 9, 3, 4, 0, 5, 4, 2, 7, 3, 2, 3, 0, 0, 5, 5, 9, 0, 3, 0, 9, 4, 9, 0, 0, 1, 3, 8, 7, 8, 6, 1, 7, 2, 0, 0, 4, 6, 8, 4, 0, 8, 9, 4, 7, 7, 2, 3, 1, 5, 6, 4, 6, 6, 0, 2, 1, 3, 7, 0, 3, 2, 9, 6, 6, 5, 4, 4, 3, 3, 1, 7, 4, 9, 6, 9, 0
(list; cons; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.
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LINKS
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M. R. Burns, MRB constant
M. R. Burns, Maple Primes
M. R. Burns, Update on the MRB Constant 1. [History and facts]
M. R. Burns, Update on the MRB Constant 2. [Explicit decimal expansions]
M. R. Burns, Update on the MRB Constant 3. [Sinusoidal characteristic]
M. R. Burns, Update on the MRB Constant 4. [250000 digits]
S. R. Finch, Iterated Exponential Constants
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Eric Weisstein's World of Mathematics, MRB Constant [From Eric W. Weisstein (eric(AT)weisstein.com), May 01 2009]
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EXAMPLE
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0.187859642462067120248517934...
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MAPLE
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evalf(sum((-1)^n*(n^(1/n)-1), n=1..infinity), 100); [From Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Jun 07 2009]
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MATHEMATICA
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e=50; ClearAll[a]; Clear[m, n, s, d]; n=131(Ceiling[e/100]); a[0]=1; For[m=1, m<n, a[m]=(1+m)^(1/(1+m)); m++ ]; Block[{$MaxExtraPrecision=e+1}, d=(3+Sqrt[8])^n; d=(d+1/d)/2; b=-1; c=-1 d; s=0; For[k=0, k<n, c=b-c; b=(k+n)(k-n)b/((k+1/2)(k+1)); s=s+c*a[k]; k++ ]]; Print[N[1/2-s/d, e]]; ClearAll[a]; Clear[m, n, s, d]; (e is the number of digits desired). - Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Aug 05 2007
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PROGRAM
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(PARI) sumalt(x=1, (-1)^x*((x^(1/x))-1))
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CROSSREFS
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A052110, A157852, A160755 [From Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Jun 07 2009]
Sequence in context: A010529 A086911 A103984 this_sequence A094106 A021536 A094082
Adjacent sequences: A037074 A037075 A037076 this_sequence A037078 A037079 A037080
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KEYWORD
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cons,nonn
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AUTHOR
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Marvin Ray Burns (bmmmburns(AT)sbcglobal.net). Entry updated Jan 30 2009, Jun 21 2009
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