KaprekarNumbers

The Kaprekar numbers $1, 9, 45, 55, 99, 297, …$ : $n$ whose square splits into a left and a (nonzero) right part that sum back to $n$ .

KaprekarNumbersthe

n

for which some split of

n^2

's decimal digits sums back to

n

, an infinite indexed collection.

Domain: Collections

Details

A lazy indexed collection: $Count(KaprekarNumbers) = +\infty$ -- every repunit-of-nines $10^k - 1$ qualifies, since $(10^k-1)^2$ splits at position $k$ into $10^k - 2$ and the last $k$ digits, summing to $10^k - 1$ . OEIS A006886.
$At(KaprekarNumbers, k)$ unranks by scanning forward from the last cached match, trying every split position (the split isn't always at $n$ 's own digit count -- $4879^2 = 23804641$ splits as $238 + 4641$ , not $2380+4641$ ) -- $At(KaprekarNumbers, 3) = 45$ ( $45^2=2025 \to 20+25$ ).
Membership goes through Element: $Element(297, KaprekarNumbers)$ is true ( $297^2=88209 \to 88+209=297$ ), $Element(298, KaprekarNumbers)$ is false.

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS