PerniciousNumbers

The pernicious numbers $3, 5, 6, 7, 9, …$: positive integers whose binary popcount is itself prime.

OEISA052294↗

PerniciousNumbersthe $n$ with $\mathrm{popcount}(n)$ prime, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(PerniciousNumbers) = +\infty$ -- every $n$ with exactly two 1-bits already qualifies (popcount 2 is prime), and there are infinitely many. OEIS A052294.
• $At(PerniciousNumbers, k)$ unranks by scanning forward -- $At(PerniciousNumbers, 1) = 3$.
• Membership goes through Element: $Element(7, PerniciousNumbers)$ is true (popcount 3, prime), $Element(15, PerniciousNumbers)$ is false (popcount 4).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, EvilNumbers, OdiousNumbers, PrimeNumbers