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

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, 13, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 25, 26, 27, 27, 28

Offset: 1

Author

N. J. A. Sloane, R. K. Guy

Keywords

• nonn
• easy
• nice

Comments

a(n) - a(n-1) = 0 or 1 (see the 1991 Monthly reference). - Emeric Deutsch, Jun 06 2005

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20.
• R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
• R. K. Guy and N. J. A. Sloane, Correspondence, 1988.
• D. Kleitman, Solution to Problem E3274, Amer. Math. Monthly, 98 (1991), 958-959.

Crossrefs

Cf. A004001, A005185, A005707.

Programs

Haskell

a005350 n = a005350_list !! (n-1)
a005350_list = 1 : 1 : 1 : h 4 1 where
   h x y = z : h (x + 1) z where z = a005350 y + a005350 (x - y)
-- Reinhard Zumkeller, Jul 20 2012

Maple

A005350 := proc(n) option remember; if n<=3 then 1 else procname(procname(n-1)) + procname(n-procname(n-1)); end if; end proc:
seq(A005350(n),n=1..64) ;

Mathematica

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 *)

SageMath

@CachedFunction
def a(n): return 1 if (n<4) else a(a(n-1)) + a(n-a(n-1))
[a(n) for n in range(1,100)]  # G. C. Greubel, Nov 14 2022