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Search: id:A164985
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| A164985 |
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Denominators of ternary BBP-type series for log(5) |
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+0
4
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| 1, 6, 27, 405, 1458, 5103, 59049, 196830, 649539, 6908733, 22320522, 71744535, 731794257, 2324522934, 7360989291, 73222472421, 230127770466, 721764371007, 7060738412025, 22029503845518, 68630377364883, 663426981193869
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The formula
log(5)=(4/27)Sum(k>=0,(1/81^k)(9/(4k+1)+3/(4k+2)+1/(4k+3)))
can be written in unit numerators:
log(5)=(4/3)Sum(k>=0,(1/81^k)(1/(4k+1)+1/(3*(4k+2))+1/(9*(4k+3)))),
so the sequence of denominators inside the sum satisfies
Sum(n>=0,1/a(n))=(3/4)log(5)
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FORMULA
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G.f.: (1+6*x+27*x^2+243*x^3+486*x^4+729*x^5)/(1-81*x^3)^2
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PROGRAM
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(PARI) a(n)=[(n\3*4+1), 3*(n\3*4+2), 9*(n\3*4+3)][n%3+1]*81^(n\3)
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CROSSREFS
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Cf. A154920.
Sequence in context: A092854 A060977 A047778 this_sequence A048436 A006174 A064810
Adjacent sequences: A164982 A164983 A164984 this_sequence A164986 A164987 A164988
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KEYWORD
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frac,nonn
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 03 2009
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