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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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 (mathar(AT)strw.leidenuniv.nl), Oct 25 2008]
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LINKS
| 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
| 1.9659482366454853371899373759344013961513271774568613932369345084422527128718868817348\
186655546304720213095034132297134791379059240045409059857526540413786057641209763864098\
463585220824067692620482074...
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CROSSREFS
| 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
| cons,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 29 2005
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