A346218 Expansion of 1/Pi in signed binary nonadjacent form.

0, 0, 1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0

Offset

1

Comments

The signed binary nonadjacent form is also called "canonical signed digit representation" or the result of a "canonical recoding" algorithm.

It is used to multiply binary numbers by the minimum number of shifts and additions or subtractions.

Multiplication by 1/Pi or, more generally, by 2^k/Pi, can be used in argument reduction in the evaluation of trigonometric functions.

References

I. Koren, Computer Arithmetic Algorithms, 2nd edition, page 146.

Links

Table of n, a(n) for n=1..84.

Thomas König, Program in C to calculate the digits using gmp and mpfr

H. Prodinger, On binary representations of integers with digits -1,0,1, Integers 0 (2000), #A08.

Wikipedia, Canonical signed digit

Wikipedia, Non-adjacent form

Example

0.01010010T0000T010T000010...

Crossrefs

Cf. A184615, A184616 (for the nonadjacent form), A049541 (1/Pi in decimal), A345703 (Pi in signed binary nonadjacent form), A127266 (1/Pi in binary).

Sequence in context: A287931 A289074 A289242 * A188037 A144598 A144606

Adjacent sequences: A346215 A346216 A346217 * A346219 A346220 A346221

Keyword

sign,easy,base

Author

Thomas König, Jul 11 2021

Status

approved