A082560 a(1)=1, a(n)=2*a(n-1) if n is odd, or a(n)=a(n/2)+1 if n is even.

1, 2, 4, 3, 6, 5, 10, 4, 8, 7, 14, 6, 12, 11, 22, 5, 10, 9, 18, 8, 16, 15, 30, 7, 14, 13, 26, 12, 24, 23, 46, 6, 12, 11, 22, 10, 20, 19, 38, 9, 18, 17, 34, 16, 32, 31, 62, 8, 16, 15, 30, 14, 28, 27, 54, 13, 26, 25, 50, 24, 48, 47, 94, 7, 14, 13, 26, 12, 24, 23, 46, 11, 22, 21, 42, 20

Offset: 1

Author

Benoit Cloitre, May 04 2003

Keywords

• nonn
• tabf
• look

Comments

b(1)=1, b(n)=2*b(n/2) if n is even, or b(n)=b(n-1)+1 if n is odd produces the sequence of natural numbers.

Seen as a triangle read by rows: T(1,1) = 1; T(n+1,2*k-1) = T(n,k)+1 and T(n+1,2*k) = 2*T(n,k)+2, 1 <= k <= 2^n. - Reinhard Zumkeller, May 13 2015

Examples

			.  1:                                 1
.  2:                 2                                4
.  3:        3               6                5                10
.  4:    4       8       7       14       6       12       11       22
.  5:  5  10   9  18   8  16  15   30   7  14  13   26  12   24  23   46
		

Links

• Reinhard Zumkeller, Rows n = 1..13 of triangle, flattened

Crossrefs

Cf. A000079 (row lengths), A033484 (right edges), A166060 (row sums), A232642 (duplicates removed).

Programs

Haskell

a082560 n k = a082560_tabf !! (n-1) !! (k-1)
a082560_row n = a082560_tabf !! (n-1)
a082560_tabf = iterate (concatMap (\x -> [x + 1, 2 * x + 2])) [1]
a082560_list = concat a082560_tabf
-- Reinhard Zumkeller, May 13 2015

PARI

a(n)=if(n<2,1,if(n%2,2*a(n-1),1+a(n/2)))

Formula

if n is in A010737 : a(n)=n-1