LuckyNumbers

The lucky numbers $1, 3, 7, 9, 13, …$ -- survivors of Ulam's positional sieve -- as a lazy indexed collection.

OEISA000959↗

LuckyNumbersthe survivors of Ulam's sieve, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(LuckyNumbers) = +\infty$, and $At$ unranks the $k$-th by running the sieve out far enough -- start from the odd numbers, then repeatedly take the smallest surviving number past $1$ as a step and delete every step-th survivor, until enough terms remain.
• OEIS A000959. Despite the name, luckiness has nothing to do with primality; the sieve's mechanics happen to leave a prime-like density behind, a coincidence number theorists still find useful for testing conjectures like a lucky-number Goldbach analogue.
• Membership goes through Element: $Element(13, LuckyNumbers)$ is true, $Element(11, LuckyNumbers)$ is false ($11$ is sieved out at the step-$3$ pass).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, PrimeNumbers