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A003160 a(1)=a(2)=1, a(n)=n-a(a(n-1))-a(a(n-2)).
(Formerly M0446)
4
1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 34, 35, 36, 36, 36, 37, 37, 37, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sequence of indices n where a(n-1)<a(n) appears to be given by A003156. [From Joerg Arndt, May 11 2010]

REFERENCES

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Representations for a special sequence, Fib. Quart., 10 (1972), 499-518, 550.

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) is asymptotic to n/2.

PROG

(PARI) a(n)=if(n<3, 1, n-a(a(n-1))-a(a(n-2)))

(Haskell)

a003160 n = a003160_list !! (n-1)

a003160_list = 1 : 1 : zipWith (-) [3..] (zipWith (+) xs $ tail xs)

   where xs = map a003160 a003160_list

-- Reinhard Zumkeller, Aug 02 2013

CROSSREFS

Cf. A005206.

Cf. A095774, A095775.

Sequence in context: A239683 A132913 A278814 * A060740 A145339 A123273

Adjacent sequences:  A003157 A003158 A003159 * A003161 A003162 A003163

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by Benoit Cloitre, Jan 01 2003

STATUS

approved

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Last modified March 24 20:06 EDT 2017. Contains 283993 sequences.