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Search: id:A006276
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| A006276 |
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A predictable Pierce expansion.
(Formerly M1298)
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+0
9
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| 2, 4, 17, 19, 5777, 5779, 192900153617, 192900153619, 7177905237579946589743592924684177, 7177905237579946589743592924684179, 36982235641841494414368017322142689171691667902755797793892925803149012751420714\ 3830378340325399155217
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. O. Shallit, Some predictable Pierce expansions, Fib. Quart., 22 (1984), 332-335.
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LINKS
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J. O. Shallit, Some predictable Pierce expansions, Fib. Quart., 22 (1984), 332-335.
Eric Weisstein's World of Mathematics, Pierce Expansion
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FORMULA
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Let c(0)=3, c(n+1) = c(n)^3-3*c(n) [A001999]; then this sequence is c(0)-1, c(0)+1, c(1)-1, c(1)+1, c(2)-1, c(2)+1, ......
a(n) = 2*F(2*3^floor(n/2)+1)-F(2*3^floor(n/2))-(-1)^n where F(k) denotes the k-th Fibonacci number A000045(k)
Let u(0)=(1+sqrt(5))/2 and u(n+1)=u(n)/frac(u(n)) where frac(x) is the fractional part of x, then a(n)=floor(u(n)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2004
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PROGRAM
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(PARI) r=(1+sqrt(5))/2; for(n=1, 10, r=r/(r-floor(r)); print1(floor(r), ", "))
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CROSSREFS
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Sequence in context: A105510 A155951 A118242 this_sequence A103051 A095018 A081356
Adjacent sequences: A006273 A006274 A006275 this_sequence A006277 A006278 A006279
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 19 2000
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