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

1,2

Links

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

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)

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 *)

Prog

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

Crossrefs

Cf. A135416.

Sequence in context: A143089 A275314 A161857 * A296075 A318678 A119674

Adjacent sequences: A135530 A135531 A135532 * A135534 A135535 A135536

Keyword

nonn,easy

Author

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

Status

approved