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A103814
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Pentanacci constant: decimal expansion of limit of A001591(n+1)/A001591(n).
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7
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1, 9, 6, 5, 9, 4, 8, 2, 3, 6, 6, 4, 5, 4, 8, 5, 3, 3, 7, 1, 8, 9, 9, 3, 7, 3, 7, 5, 9, 3, 4, 4, 0, 1, 3, 9, 6, 1, 5, 1, 3, 2, 7, 1, 7, 7, 4, 5, 6, 8, 6, 1, 3, 9, 3, 2, 3, 6, 9, 3, 4, 5, 0, 8, 4, 4, 2, 2, 5, 2, 7, 1, 2, 8, 7, 1, 8, 8, 6, 8, 8, 1, 7, 3, 4, 8, 1, 8, 6, 6, 5, 5, 5, 4, 6, 3, 0, 4, 7, 2, 0, 2, 1, 3, 0
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OFFSET
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1,2
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COMMENTS
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The pentanacci constant P is the limit as n -> infinity of the ratio of Pentanacci(n+1)/Pentanacci(n) = A001591(n+1)/A001591(n), which is the principal root of x^5-x^4-x^3-x^2-x-1 = 0. Note that we have: P + P^-5 = 2.
The pentanacci constant corresponds to the Golden Section in a fivepartite division 1 = u_1 + u_2 + u_3 + u_4 + u_5 of a unit line segment, i.e. if 1/u_1 = u_1/u_2 = u_2/u_3 = u_3/u_4 + u_4/u_5 = c, c is the pentanacci constant. - Seppo Mustonen, Apr 19 2005
The other 4 roots of the polynomial 1+x+x^2+x^3+x^4-x^5 are the two complex-conjugated pairs -0.6783507129699967... +- i * 0.458536187273144499.. and 0.1953765946472540452... +- i * 0.848853640546245551858... [From R. J. Mathar, Oct 25 2008]
The continued fraction expansion is 1, 1, 28, 2, 1, 2, 1, 1, 1, 2, 4, 2, 1, 3, 1, 6, 1, 4, 1, 1, 5, 3, 2, 15, 69, 1, 1, 14, 1, 8, 1, 6,... - R. J. Mathar, Mar 09 2012
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LINKS
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Table of n, a(n) for n=1..105.
Eric Weisstein et al., Tetranacci Constant.
Eric Weisstein's World of Mathematics, Pentanacci Constant
Eric Weisstein's World of Mathematics, Pentanacci Number
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FORMULA
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1.9659482366454853371899373759344013961513271774568613932369345084422527128718868817348\
186655546304720213095034132297134791379059240045409059857526540413786057641209763864098\
463585220824067692620482074...
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CROSSREFS
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Cf. A001591, A058265, A086088.
Sequence in context: A102047 A144665 A019884 * A117020 A011459 A100044
Adjacent sequences: A103811 A103812 A103813 * A103815 A103816 A103817
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Vos Post, Mar 29 2005
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STATUS
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approved
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