A005707 a(1) = a(2) = a(3) = a(4) = 1, a(n) = a(a(n-1))+a(n-a(n-1)) for n >= 5. (Formerly M0251)

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

1,5

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.

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 *)

Prog

(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

Crossrefs

Cf. A004001, A005350.

Cf. A005185.

Sequence in context: A132073 A087817 A091497 * A087828 A330779 A366632

Adjacent sequences: A005704 A005705 A005706 * A005708 A005709 A005710

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Jun 06 2005

Status

approved