HappyNumbers

The happy numbers $1, 7, 10, 13, 19, …$ : iterating sum-of-squared-digits reaches 1.

HappyNumbersthe

n

whose sum-of-squared-digits iteration reaches 1 (rather than the other cycle,

\{4,16,37,58,89,145,42,20\}

), an infinite indexed collection.

Domain: Collections

Details

A lazy indexed collection: $Count(HappyNumbers) = +\infty$ . OEIS A007770.
$At(HappyNumbers, k)$ unranks by scanning forward from the last cached match -- $At(HappyNumbers, 5) = 19$ .
Membership goes through Element: $Element(7, HappyNumbers)$ is true ( $7 \to 49 \to 97 \to 130 \to 10 \to 1$ ), $Element(4, HappyNumbers)$ is false (the other cycle).

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS