A135533 Guy Steele's sequence GS(4,6) (see A135416).

1, 2, 3, 3, 5, 4, 7, 4, 7, 6, 11, 5, 9, 8, 15, 5, 9, 8, 15, 7, 13, 12, 23, 6, 11, 10, 19, 9, 17, 16, 31, 6, 11, 10, 19, 9, 17, 16, 31, 8, 15, 14, 27, 13, 25, 24, 47, 7, 13, 12, 23, 11, 21, 20, 39, 10, 19, 18, 35, 17, 33, 32, 63, 7, 13, 12, 23, 11, 21, 20, 39, 10, 19, 18, 35, 17, 33, 32, 63

Offset: 1

Author

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

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A135416.

Programs

Maple

GS(4,6,200); [see A135416].

Mathematica

i = 4; j = 6; 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, 79] (* Jean-François Alcover, Sep 12 2013 *)

PARI

a(n)=if(n<4, return(n)); (1+n%2)*a(n\2) + 1 \\ Charles R Greathouse IV, Oct 17 2016

Formula

From Don Knuth, Mar 01 2008: (Start)

a(n) = Sum_{k=0..A000523(n)} 2^A000120(n mod 2^k).

a(n) = 1 + A000523(n) * 2^A000120(n) - A135586(n). (End)