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A003160 a(1) = a(2) = 1, a(n) = n - a(a(n-1)) - a(a(n-2)).
(Formerly M0446)
7
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. - Joerg Arndt, May 11 2010
The number n appears A080426(n+1) times. - John Keith, Dec 31 2020
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr., Representations for a special sequence, Fibonacci Quarterly 10.5 (1972), 499-518, 550.
FORMULA
a(n) is asymptotic to n/2.
MATHEMATICA
Block[{a = {1, 1}}, Do[AppendTo[a, i - a[[ a[[-1]] ]] - a[[ a[[-2]] ]] ], {i, 3, 76}]; a] (* Michael De Vlieger, Dec 31 2020 *)
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
(SageMath)
@CachedFunction
def a(n): return 1 if (n<3) else n - a(a(n-1)) - a(a(n-2))
[a(n) for n in range(1, 81)] # G. C. Greubel, Nov 06 2022
CROSSREFS
Sequence in context: A239683 A132913 A278814 * A060740 A307467 A145339
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Benoit Cloitre, Jan 01 2003
STATUS
approved

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Last modified May 27 12:27 EDT 2024. Contains 372858 sequences. (Running on oeis4.)