A003160 a(1) = a(2) = 1, a(n) = n - a(a(n-1)) - a(a(n-2)). (Formerly M0446)

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

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

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

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

Cf. A003156, A005206, A080426, A095774, A095775.

Sequence in context: A239683 A132913 A278814 * A060740 A307467 A145339

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