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A005350 a(1) = a(2) = a(3) = 1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n >= 4.

%I A005350 M0253 #41 Mar 27 2024 08:40:44
%S A005350 1,1,1,2,2,3,3,3,4,5,5,5,5,6,7,7,8,8,8,8,8,9,10,11,11,12,12,12,13,13,
%T A005350 13,13,13,13,14,15,16,16,17,18,18,19,19,19,20,20,20,20,21,21,21,21,21,
%U A005350 21,21,22,23,24,25,25,26,27,27,28
%N A005350 a(1) = a(2) = a(3) = 1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n >= 4.
%C A005350 a(n) - a(n-1) = 0 or 1 (see the 1991 Monthly reference). - _Emeric Deutsch_, Jun 06 2005
%D A005350 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005350 T. D. Noe, <a href="/A005350/b005350.txt">Table of n, a(n) for n = 1..1000</a>
%H A005350 R. K. Guy, <a href="http://www.jstor.org/stable/2691503">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20.
%H A005350 R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
%H A005350 R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.
%H A005350 D. Kleitman, <a href="http://www.jstor.org/stable/2324158">Solution to Problem E3274</a>, Amer. Math. Monthly, 98 (1991), 958-959.
%p A005350 A005350 := proc(n) option remember; if n<=3 then 1 else procname(procname(n-1)) + procname(n-procname(n-1)); end if; end proc:
%p A005350 seq(A005350(n),n=1..64) ;
%t A005350 a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[a[n-1]] + a[n-a[n-1]]; Table[a[n], {n, 1, 64}] (* _Jean-François Alcover_, Feb 11 2014 *)
%o A005350 (Haskell)
%o A005350 a005350 n = a005350_list !! (n-1)
%o A005350 a005350_list = 1 : 1 : 1 : h 4 1 where
%o A005350    h x y = z : h (x + 1) z where z = a005350 y + a005350 (x - y)
%o A005350 -- _Reinhard Zumkeller_, Jul 20 2012
%o A005350 (SageMath)
%o A005350 @CachedFunction
%o A005350 def a(n): return 1 if (n<4) else a(a(n-1)) + a(n-a(n-1))
%o A005350 [a(n) for n in range(1,100)]  # _G. C. Greubel_, Nov 14 2022
%Y A005350 Cf. A004001, A005185, A005707.
%K A005350 nonn,easy,nice
%O A005350 1,4
%A A005350 _N. J. A. Sloane_, _R. K. Guy_