Unbounded nested number sequences

UNNS — Interactive Dependency Explorer (+Exports & Graph)

UNNS — Dependency Explorer

Core Calc u, block, shift Integer Zones M=kN Cross-Nest Search equality Value Clustering mod k Recursive Curiosities (N+1)^2 Self-Tests assertions

About

Interactive implementation of UNNS Framework: Deep Dependencies & Curiosities. Uses s_N(M)= M*(N+1)^2 / N and BigInt equality. Now with CSV/PNG exports, schematic graph view, and shareable URL hash.

Core Calculator

N (nest)

M (position)

Modulus k (for hue/cluster)

Integer Zones (M = kN)

For a fixed N, s_N(M) is integer exactly when N | M. Then s_N(kN)=k*(N+1)^2.

N

M range [a..b]

Cross-Nest Search (Exact Equality)

Given (N₁,M₁), find all (N₂,M₂) with equal value. Uses exact cross-multiplication: M₁(N₁+1)²N₂ = M₂(N₂+1)²N₁. Below is a schematic grid/tree layout connecting matches to the target.

Target N₁

Target M₁

N₂ range

M₂ range

Value Clustering (mod k)

Color the grid of (N,M) by s_N(M) mod k. Adjust the grid and modulus to reveal clustering patterns.

N size

M size

Modulus k

Recursive Curiosities

Diagonal identity: s_N(N) = (N+1)^2.

List N from

to

Self-Tests (Assertions)

Quick checks to validate identities.

Press G to jump to the top.