A274576 a(2n) = floor(n/2), a(2n+1) = a(n), a(0)=0.

0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 3, 1, 3, 0, 4, 2, 4, 1, 5, 2, 5, 0, 6, 3, 6, 1, 7, 3, 7, 0, 8, 4, 8, 2, 9, 4, 9, 1, 10, 5, 10, 2, 11, 5, 11, 0, 12, 6, 12, 3, 13, 6, 13, 1, 14, 7, 14, 3, 15, 7, 15, 0, 16, 8, 16, 4, 17, 8, 17, 2, 18, 9, 18, 4, 19, 9, 19, 1, 20, 10, 20, 5, 21, 10, 21, 2, 22, 11, 22, 5, 23, 11, 23, 0, 24, 12, 24, 6, 25, 12, 25, 3, 26, 13, 26, 6, 27, 13

Offset

0,9

Comments

Self-similar or fractal sequence (underlining every second or fourth term, reproduce the original sequence).

Links

Table of n, a(n) for n=0..109.

Michael Gilleland, Some Self-Similar Integer Sequences

Formula

a(2n) = a(4n+1) = A004526(n).

a(4n) = a(4n+2) = A001477(n).

a(2n+1) = a(4n+3) = a(n).

a(2^k*n) = 2^(k-2)*n, k>1.

Example

a(0) = 0;
a(1) = a(2*0+1) = a(0) = 0;
a(2) = a(2*1) = floor(1/2) = 0,
a(3) = a(2*1+1) = a(1) = 0;
a(4) = a(2*2) = floor(2/2) = 1;
a(5) = a(2*2+1) = a(2) = 0;
a(6) = a(2*3) = floor(3/2) = 1, etc.
...........................................
a(n)    = 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, ...
a(2n+1) = 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, ...
a(4n+3) = 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, ...
a(2n)   = 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...
a(4n+1) = 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...
a(4n)   = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
a(4n+2) = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
...........................................

Mathematica

Table[BitShiftRight[n, IntegerExponent[n, 2] + 2], {n, 100}]

Crossrefs

Cf. A000265, A001285, A001477, A004526, A003602, A005590, A025480.

Sequence in context: A257460 A339471 A159834 * A257081 A271484 A199920

Adjacent sequences: A274573 A274574 A274575 * A274577 A274578 A274579

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jun 29 2016

Status

approved