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A007570 a(n) = F(F(n)), where F is a Fibonacci number.
(Formerly M1537)
21
0, 1, 1, 1, 2, 5, 21, 233, 10946, 5702887, 139583862445, 1779979416004714189, 555565404224292694404015791808, 2211236406303914545699412969744873993387956988653, 2746979206949941983182302875628764119171817307595766156998135811615145905740557 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Asymptotic behavior as n->infinity: a(n+1)=a(n)*phi^(F(n-1)), with phi = A001622 = 1.61803... (golden ratio). - Carmine Suriano, Jan 24 2011

REFERENCES

E. A. Parberry, Two recursion relations for F(F(n)), Fib. Quart., 15 (1977), 122 and 139.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..19 (terms n = 0..17 from T. D. Noe)

C. Street, A Recurrence for the Sequence {F(F(n)),n=>0}

MAPLE

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:

a:= n-> F(F(n)):

seq(a(n), n=0..14);  # Alois P. Heinz, Oct 09 2015

MATHEMATICA

F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2]; Table[ F[ F[n] ], {n, 0, 14} ]

Fibonacci[Fibonacci[Range[0, 20]]] (* Harvey P. Dale, May 05 2012 *)

PROG

(Sage) [fibonacci(fibonacci(n)) for n in xrange(0, 14)] # Zerinvary Lajos, Nov 30 2009

(PARI) a(n)=fibonacci(fibonacci(n)) \\ Charles R Greathouse IV, Feb 03 2014

CROSSREFS

Cf. A000045, A005371, A058051.

Sequence in context: A108021 A162437 A216756 * A173313 A210575 A174143

Adjacent sequences:  A007567 A007568 A007569 * A007571 A007572 A007573

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

One more term from Harvey P. Dale, May 05 2012

STATUS

approved

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Last modified March 23 12:38 EDT 2017. Contains 283951 sequences.