A153036 Integer parts of the full Stern-Brocot tree.

0, 1, 0, 2, 0, 0, 1, 3, 0, 0, 0, 0, 1, 1, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,4

Links

Table of n, a(n) for n=0..105.

Jon Maiga, Computer-generated formulas for A153036, Sequence Machine.

N. J. A. Sloane, Stern-Brocot or Farey Tree

Index entries for sequences related to Stern's sequences

Formula

a(n+1) = floor(A007305(n+2)/A047679(n)). [Corrected by Andrey Zabolotskiy, Jul 23 2020]

a(n) = if n=2^k-1 then k else Log2(n)-1-Log2(2^(Log2(n)+1)-(n+1)), where Log2=A000523.

From Andrey Zabolotskiy, Oct 07 2021: (Start)

Formulas discovered by Sequence Machine (and also essentially by Kevin Ryde):

a(n) = A090996(n) - A043545(n).

a(n) = A007814(A145342(n+1)). (End)

Example

a(1): 1;
a(2..3): 1x0, 2;
a(4..7): 2x0, 1x1, 3;
a(8..15): 4x0, 2x1, 1x2, 4;
a(16..31): 8x0, 4x1, 2x2, 1x3, 5;
a(32..63): 16x0, 8x1, 4x2, 2x3, 1x4, 6;
a(64..127): 32x0, 16x1, 8x2, 4x3, 2x4, 1x5, 7;
a(128..255): 64x0, 32x1, 16x2, 8x3, 4x4, 2x5, 1x6, 8;
a(256..511): 128x0, 64x1, 32x2, 16x3, 8x4, 4x5, 2x6, 1x7, 9.

Crossrefs

Cf. A130321.

If every block of terms of length 2^k is reversed, we get A290256; other permutations within these blocks give A007814 and A272729-1.

Cf. A090996, A043545, A007814, A145342.

Sequence in context: A284608 A325201 A260019 * A258651 A350530 A258850

Adjacent sequences: A153033 A153034 A153035 * A153037 A153038 A153039

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Dec 22 2008

Extensions

a(0) = 0 added by Andrey Zabolotskiy, Jul 23 2020

Status

approved