A135529 Guy Steele's sequence GS(4,5) (see A135416).

1, 2, 2, 3, 4, 3, 4, 4, 6, 5, 8, 4, 6, 5, 8, 5, 8, 7, 12, 6, 10, 9, 16, 5, 8, 7, 12, 6, 10, 9, 16, 6, 10, 9, 16, 8, 14, 13, 24, 7, 12, 11, 20, 10, 18, 17, 32, 6, 10, 9, 16, 8, 14, 13, 24, 7, 12, 11, 20, 10, 18, 17, 32, 7, 12, 11, 20, 10, 18, 17, 32, 9, 16, 15, 28, 14, 26, 25, 48, 8, 14, 13, 24

Offset: 1

Author

N. J. A. Sloane, based on a message from Guy Steele and Don Knuth, Mar 01 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A135416.

Programs

Maple

GS(4,5,200); # [see A135416].

Mathematica

i = 4; j = 5; Clear[a]; a[1] = 1; a[n_?EvenQ] := a[n] = {0, 1, a[n/2], a[n/2]+1, 2*a[n/2], 2*a[n/2]+1}[[i]]; a[n_?OddQ] := a[n] = {0, 1, a[(n-1)/2], a[(n-1)/2]+1, 2*a[(n-1)/2], 2*a[(n-1)/2]+1}[[j]]; Array[a, 83] (* Jean-François Alcover, Sep 12 2013 *)

Formula

a(n) = A135533(n) + 1 - 2^(A000120(n)-1). - Don Knuth, Mar 01 2008