SexyPrimes

The (lesser) sexy primes $5, 7, 11, 13, 17, …$ : primes $p$ with $p+6$ also prime.

SexyPrimesthe lesser prime

p

of a sexy pair

(p, p+6)

, an indexed collection of open infinitude.

Domain: Collections

Details

A lazy indexed collection; open infinitude, so $Count(SexyPrimes) = NaN$ . OEIS A023201 (the lesser member; named for the Latin \emph{sex}, six).
$At(SexyPrimes, k)$ unranks by scanning forward, testing primality of $n$ and $n+6$ -- $At(SexyPrimes, 1) = 5$ .
Membership goes through Element: $Element(5, SexyPrimes)$ is true ( $5, 11$ both prime), $Element(7, SexyPrimes)$ is true too ( $7,13$ ); $Element(9, SexyPrimes)$ is false (not prime).
$SexyPrimes$ is $PrimePairs(6)$ verbatim.

Enumeration

Basic #

The first 20 lesser sexy primes, OEIS A023201

\mathrm{Take}(\mathrm{SexyPrimes}, 20)

Out

\bigl\lbrack5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131\bigr\rbrack

About

Examples	1
Crosswalk	OEIS