A345703 Expansion of Pi in signed binary nonadjacent form.

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

Offset

3

Comments

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

References

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

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

Links

Table of n, a(n) for n=3..85.

Wikipedia, Canonical signed digit

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

Example

10T.0010010001000000T0T010101000100010001...

Crossrefs

Cf. A184615, A184616 (for the nonadjacent form), A004601 (binary expansion of Pi), A331313 (balanced ternary expansion of Pi).

Sequence in context: A351725 A243148 A089495 * A365807 A173857 A114482

Adjacent sequences: A345700 A345701 A345702 * A345704 A345705 A345706

Keyword

sign,easy,base

Author

Thomas König, Jun 24 2021

Status

approved