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Search: id:A073668
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| A073668 |
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Decimal expansion of Sum(k=1..inf, 1/(10^k-1)). |
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+0
6
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| 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 3, 0, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 3, 2, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 3, 2, 2, 4, 6, 6, 4, 8, 3, 0, 5, 4, 3, 2, 4, 4, 4, 8, 3, 2, 4, 6, 4, 4, 5, 2, 2, 6, 6, 9, 2, 8, 2, 8, 8
(list; cons; graph; listen)
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OFFSET
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0,2
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COMMENT
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Parallels A000005 up to a(46).
Sum{k = 1 to infinity}, x^k/(1-x^k) = sum{k = 1 to infinity},tau(k)*x^k. Choosing x = 1/10 gives the result. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 21 2002
Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Mar 11 2009: (Start)
=Sum_{k=1..inf}, 1/((2^k*5^k)-1)
=Sum_{k=1..inf}, (1/2^k)*(1/5^k)/(1-((1/2^k)*(1/5^k)))
Sum_{k=1..inf},1/(5^k) = 1/4
Sum_{k=1..inf},1/(2^k) = 1
Sum_{k=1..inf},(1/5^k)/(1-((1/2^k)*(1/5^k)))=0,2726344339156...
Sum_{k=1..inf},(1/2^k)/(1-((1/2^k)*(1/5^k)))=1,0582125127815...
Sum_{k=1..inf}, 1/(1-((1/2^k)*(1/5^k))) = k + A073668
(End)
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REFERENCES
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Amarnath Murthy, Some interesting results on d(N), the number of divisors of a natural number, page 463, Octogon Mathematical Magazine, Vol. 8 No. 2,October 2000.
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EXAMPLE
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0.122324243426244526264428344628264449244... = A065444/9.
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MATHEMATICA
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RealDigits[ N[ Sum[1/(10^k - 1), {k, 1, Infinity}], 120]] [[1]]
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CROSSREFS
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Sequence in context: A000005 A122667 A122668 this_sequence A066800 A114102 A144373
Adjacent sequences: A073665 A073666 A073667 this_sequence A073669 A073670 A073671
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KEYWORD
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cons,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 29 2002
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