A005707 a(1) = a(2) = a(3) = a(4) = 1, a(n) = a(a(n-1))+a(n-a(n-1)) for n >= 5.

1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 8, 9, 9, 9, 9, 9, 9, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 27

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

It is known that 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
• D. Kleitman, Solution to Problem E3274, Amer. Math. Monthly, 98 (1991), 958-959.
• R. K. Guy, Letter to N. J. A. Sloane with attachment, 1988
• R. K. Guy and N. J. A. Sloane, Correspondence, 1988.
• D. Newman, Problem E3274, Amer. Math. Monthly, 95 (1988), 555.

Crossrefs

Cf. A004001, A005350.

Cf. A005185.

Programs

Haskell

a005707 n = a005707_list !! (n-1)
a005707_list = 1 : 1 : 1 : 1 : h 5 1 where
   h x y = z : h (x + 1) z where z = a005707 y + a005707 (x - y)
-- Reinhard Zumkeller, Jul 20 2012

Maple

a[1]:=1: a[2]:=1: a[3]:=1: a[4]:=1: for n from 5 to 100 do a[n]:=a[a[n-1]]+a[n-a[n-1]] od: seq(a[n],n=1..100); # Emeric Deutsch, Jun 06 2005

Mathematica

a[1]=a[2]=a[3]=a[4]=1;a[n_]:=a[n]=a[a[n-1]]+a[n-a[n-1]];Table[a[i],{i,80}] (* Harvey P. Dale, Jan 22 2013 *)

Extensions

More terms from Emeric Deutsch, Jun 06 2005