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Search: id:A126689
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| A126689 |
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Decimal expansion of negative of Granville-Soundararajan constant. |
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+0
2
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| 6, 5, 6, 9, 9, 9, 0, 1, 3, 7, 1, 6, 9, 2, 7, 8, 6, 8, 2, 7, 9, 1, 2, 0, 0, 5, 6, 8, 8, 9, 5, 7, 5, 7, 8, 0, 7, 5, 5, 4, 7, 4, 1, 9, 1, 5, 4, 0, 8, 9, 8, 3, 1, 6, 5, 7, 1, 5, 7, 7, 8, 1, 6, 3, 5, 2, 6, 0, 2, 7, 8, 8, 8, 1, 1, 3, 8, 2, 8, 4, 4, 0, 2, 4, 0, 5, 7, 6, 0, 3, 8, 2, 6, 3, 9, 8, 3, 6, 5, 3, 8, 7, 1, 5, 2
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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From Balog et al.'s abstract: "We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions."
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REFERENCES
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Andrew Granville and K. Soundararajan, The Spectrum of Multiplicative Functions, Ann. of Math., Vol. 153 (2001), pp. 407-470.
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LINKS
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Antal Balog, Andrew Granville and K. Soundararajan, Multiplicative functions in arithmetic progressions, 13 Feb 2007, p. 7.
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FORMULA
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Equals 1-2*ln[1+sqrt e]+4*Integral( [log t]/(1+t),t=1..sqrt e) = 1-ln 4+4*sum_{s=1..infinity} K(s)/(s*2^s) where K(s)=sum_{k=0..s} binomial(s,k)*(-1)^k*[exp(k/2)-1]/k . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 16 2007
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EXAMPLE
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-0.656999...
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MAPLE
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Digits := 40 ; K := proc(s) 0.5+add( binomial(s, k)*(-1)^k/k*(exp(0.5*k)-1), k=1..s) ; end: A126689 := proc(smax) 1.0-log(4.0)+add(K(s)*2^(2-s)/s, s=1..smax) ; end: for smax from 0 to 2*Digits do print(A126689(smax)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 16 2007
read("transforms3") ; Digits := 120 : x := 1+Pi^2/3+4*dilog(exp(1/2)+1) ; x := evalf(x) ; CONSTTOLIST(x) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2009]
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CROSSREFS
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Sequence in context: A023408 A133616 A019621 this_sequence A101634 A071176 A089826
Adjacent sequences: A126686 A126687 A126688 this_sequence A126690 A126691 A126692
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KEYWORD
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cons,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 16 2007
More digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2009
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