OstrowskiNumerals

Ostrowski numeration: the numeral system a continued fraction's partial quotients define, with a ceiling rule — a digit may reach its bound only if the one below it is zero — that forbids carries. All quotients equal to 1 gives the golden ratio and reduces to ZeckendorfNumerals.

OstrowskiNumerals(quotients)the system for partial quotients $a_1, a_2, \dots$

Typed signatures

Type	Package	Applies
(list<integer>) -> value	numerals	always

Domain: Numeral systems

Examples

Basic #

All quotients 1 gives Zeckendorf-style digits (places $1,1,2,3,5,8,13,21$)

live ↗

In$\mathrm{IntegerDigits}(20, \mathrm{OstrowskiNumerals}(\bigl\lbrack1, 1, 1, 1, 1, 1, 1, 1\bigr\rbrack))$Out$\bigl\lbrack0, 1, 0, 1, 0, 1, 0, 0\bigr\rbrack$

Scope #

Quotients $[2,2,2]$: places $1, 2, 5$

live ↗

In$\mathrm{IntegerDigits}(9, \mathrm{OstrowskiNumerals}(\bigl\lbrack2, 2, 2\bigr\rbrack))$Out$\bigl\lbrack1, 2, 0\bigr\rbrack$

About

Examples	2

See also: IntegerDigits, ZeckendorfNumerals, Ostrowski