Get Math Help

Home / Get Math Help

Rudin-Shapiro Sequence

Alternate name

Sequence description

-1 raised to the power of the number of 11-blocks in the binary representation of n

Sequence terms

1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, ...

Program

$a_n = (-1)^Count[Partition[IntegerDigits[n, 2], 2, 1], {1, 1}]$

Table program

$Table[(-1)^Count[Partition[IntegerDigits[k, 2], 2, 1], {1, 1}], {k, 0, n}]$

Plot