|
| |
|
|
A001999
|
|
a(n+1) = a(n)(a(n)^2 - 3).
(Formerly M3055 N1239)
|
|
3
| |
|
|
3, 18, 5778, 192900153618, 7177905237579946589743592924684178, 369822356418414944143680173221426891716916679027557977938929258031490127514207143830378340325399155218
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| The next term in the sequence contains 305 digits [from Harvey P. Dale, June 09 2011]
|
|
|
REFERENCES
| E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
Eric Weisstein's World of Mathematics, Pierce Expansion
|
|
|
FORMULA
| a(n) = 2*F(2*3^n+1)-F(2*3^n) = ceiling(tau^(2*3^n)) where F(k)=A000045(k) is the k-th Fibonacci number and tau is the golden ratio. - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
|
|
|
MATHEMATICA
| NestList[#(#^2-3)&, 3, 6] (* From Harvey P. Dale, June 09 2011 *)
|
|
|
PROG
| (PARI) a(n)=2*fibonacci(2*3^n+1)-fibonacci(2*3^n)
|
|
|
CROSSREFS
| Cf. A006276.
Sequence in context: A069854 A157556 A057133 * A157580 A101293 A189799
Adjacent sequences: A001996 A001997 A001998 * A002000 A002001 A002002
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
