Sequence Tools

Calculate the nth term and sum of arithmetic sequences with step-by-step solutions, interactive visualizations, and high-precision results up to 1000 decimal places.

Generate the n-th Catalan number with a step-by-step formula derivation, interactive parenthesization and polygon-triangulation visuals, a full sequence table and the combinatorial meaning behind each interpretation.

Explore the Collatz conjecture (3n+1 problem) by generating the hailstone sequence for any positive integer. Visualize the trajectory, analyze stopping time, peak values, and sequence statistics with interactive charts.

Generate and explore cube numbers with interactive visualizations, 3D cube diagrams, step-by-step calculations, and multiple export formats. Perfect for students, teachers, and math enthusiasts.

Enter a number from 1 to 10,000 to get a list of consecutive prime numbers, identify twin primes, and view the gaps between each prime.

Calculate the nth term, sum of first n terms, and infinite sum of any geometric sequence with step-by-step solutions and interactive visualization.

Determine if a number is a happy number by repeatedly replacing it with the sum of the squares of its digits. Visualize the happiness journey, explore patterns, and find all happy numbers in any range.

Choose a count, a maximum value, or a start and end index. See that Fibonacci list, with a golden-ratio view and a spiral diagram.

Generate a comprehensive list of prime numbers from 2 to any specified number up to 10,000. Discover the building blocks of mathematics with instant results and detailed statistics.

Generate magic squares of any order N where every row, column, and diagonal sums to the same magic constant. Includes step-by-step construction, interactive visualization, and mathematical properties.

Compute the partition function p(n), the number of ways to write n as a sum of positive integers. Enumerate every partition for small n with Young diagrams, compare distinct-parts and odd-parts counts, and plot the growth curve.

Generate Pascal's triangle up to 30 rows. Explore patterns like Fibonacci numbers, Sierpinski triangle, powers of 2, and binomial coefficients with interactive highlighting and animations.

Evaluate product (Π) pi notation expressions with step-by-step factor expansion, running product visualization, and growth analysis. Supports polynomial, exponential, trigonometric, and custom expressions.

Enter a linear homogeneous recurrence with constant coefficients and its initial values. Get the closed form and up to 60 terms.

Evaluate sigma (Σ) summation notation expressions with step-by-step term expansion, running total visualization, and convergence analysis. Supports polynomial, exponential, trigonometric, and custom expressions.

Generate list of square numbers (perfect squares), find squares in a range, or check if a number is a perfect square. Interactive visualization with step-by-step calculations.

Find every twin prime pair (primes p and p+2) up to any limit you choose. Get the complete list, totals, density per decade, the predicted Hardy-Littlewood count, largest pair found, and an interactive visualization — all in one place.