countably 2026.5.31.3020

Infinite number sequences

Lazy, immutable, infinite numeric sequences for Python.

countably lets you describe sequences declaratively, the way you’d write them on paper, and evaluate them on demand:

from countably import count, constant

triangular = count() * (count() + 1) // 2     # 0, 1, 3, 6, 10, ...
powers_of_two = 2 ** count()                  # 1, 2, 4, 8, 16, ...
every_third = count()[2::3]                   # 2, 5, 8, 11, ...

The primitives are just constant and count. Arithmetic, comparisons, slicing, and element-wise maximum / minimum build everything else. Plain numbers are coerced automatically, so 3 + 5 * count() is equivalent to constant(3) + constant(5) * count().

Highlights

• Lazy – elements are computed only on access, with a per-instance 100-item LRU cache for random access. Iteration walks the inputs directly, bypassing the cache.

• Immutable – every operation produces a new sequence; nothing is mutated.

• Iterable, not iterator – iter(seq) starts fresh every time.

• Slices are lazy too – seq[2::3] stays infinite, seq[2:10] is finite with a real len(). Arithmetic between sequences uses the shorter length.

• Round / floor / ceil / trunc are supported through the standard Python protocols (math.floor(seq), round(seq)).

• Comparisons (<, <=, >, >=) return sequences of booleans, which are numbers in the same world.

See doc/quick-start.rst for usage including a Fibonacci one-liner.

Install

pip install countably