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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

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)

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

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 July 24 05:18 EDT 2017. Contains 289717 sequences.