All 92 generators
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Sequences 44
- Counting numbers One, two, three and onward — the natural numbers in order, from any starting point, at any stride.
- Even numbers The multiples of two, from any starting point and at any even stride — the oldest classification a number can have.
- Odd numbers The integers two will not divide, from any starting point — the gnomons that build the squares, and the half of parity that folklore kept.
- Prime numbers The numbers with no divisors but themselves and one — listed in order from anywhere you like, by segmented sieve.
- Fibonacci numbers Each term is the sum of the two before it — the sequence behind spirals, sunflowers and the golden ratio.
- Square numbers The perfect squares 1, 4, 9, 16 — the running totals of the odd numbers, and the oldest figurate sequence of all.
- Cube numbers The perfect cubes 1, 8, 27, 64 — whose running totals are, remarkably, always perfect squares.
- Triangular numbers The running totals of 1, 2, 3, 4 … — the counts that stack into a filled triangle, from bowling pins to handshakes.
- Powers of two 1, 2, 4, 8, 16 — the sequence computing is built on. In decimal, binary or hex, exact however far you take it.
- Factorials n! — the product of every whole number up to n, and the count of ways to put n things in order. Exact at any size.
- Digits of pi The decimal expansion of π, computed live to as many places as you like — not copied from a lookup table.
- Unit fractions 1, 1/2, 1/3, 1/4 — the reciprocals of the counting numbers, as fractions or as exact decimals, with the harmonic total.
- Halving sequence 1, 1/2, 1/4, 1/8 — repeated halving as fractions or exact decimals, with the running total that creeps up on 2 and never arrives.
- Composite numbers Everything that is not prime and not 1 — optionally with the prime factorisation that makes it composite.
- Perfect numbers Integers that equal the sum of their own divisors — 6, 28, 496, 8128. Only 52 are known, and nobody knows whether an odd one exists.
- Collatz sequence Halve it when it is even, triple it and add one when it is odd — then watch the hailstone numbers climb and crash on their way down to 1.
- Twin primes Primes that come two apart — (3, 5), (11, 13), (17, 19) — and the open conjecture that they never run out.
- Digits of the golden ratio The decimal expansion of φ = (1 + √5)/2, computed on request from an exact integer square root.
- Digits of e The decimal expansion of Euler's number, summed from 1/k! on request to as many places as you want.
- Lucas numbers Fibonacci’s rule from a different start: 2, 1, 3, 4, 7, 11 — the sequence Édouard Lucas used to hunt for primes.
- Catalan numbers One sequence, dozens of meanings: balanced brackets, binary tree shapes, ways to cut a polygon into triangles.
- Mersenne primes Primes one less than a power of two. Only 52 are known, and the largest has over 41 million digits.
- Happy numbers Square the digits, add them up, repeat. Reach 1 and the number is happy; otherwise you fall into an eight-number loop.
- Armstrong numbers Numbers equal to the sum of their own digits raised to the power of how many digits they have. Only 88 exist in base 10.
- Palindromic primes Primes that read the same backwards — 2, 3, 5, 7, 11, 101, 131, 151 and on. Only 11 has an even number of digits.
- Prime gaps The distances between consecutive primes: 1, 2, 2, 4, 2, 4, 2, 4, 6 — including the record-setting gaps.
- Divisor counts How many divisors each number has — the function whose average value Dirichlet pinned down in 1849 and whose error term is still open.
- Divisor sums Add up a number’s divisors and you get σ(n) — the function that defines perfect, abundant and amicable numbers.
- Euler totient values φ(n) counts the numbers below n that share no factor with it — the function at the heart of Euler’s theorem and RSA.
- Abundant numbers Numbers whose divisors add up to more than the number itself — 12, 18, 20, 24. Roughly one integer in four is abundant.
- Deficient numbers Numbers whose divisors add up to less than the number itself — every prime, every prime power, and about three integers in four.
- Amicable pairs Two numbers that each add up to the other: the divisors of 220 sum to 284, and the divisors of 284 sum to 220.
- Highly composite numbers Numbers with more divisors than every smaller number — 1, 2, 4, 6, 12, 24, 36, 48, 60, 120 and on upwards.
- Pentagonal numbers 1, 5, 12, 22, 35 — the figurate numbers whose generalised form controls how every integer can be partitioned.
- Hexagonal numbers 1, 6, 15, 28, 45 — every one of them also a triangular number, and the centred form is the shape of a honeycomb.
- Tribonacci numbers Fibonacci with a longer memory: every term sums the three before it, giving 0, 1, 1, 2, 4, 7, 13, 24.
- Pell numbers Double the last term and add the one before: 0, 1, 2, 5, 12, 29, 70 — the sequence that approximates √2.
- Digits of the square root of 2 The decimal expansion of √2 — the first number proved irrational — from an exact integer square root.
- Fermat numbers F(n) = 2^(2^n) + 1. Fermat thought they were all prime; Euler found a factor of the sixth one and ended the idea.
- Sophie Germain primes Primes p where 2p + 1 is prime too. Germain invented them to attack Fermat's Last Theorem; cryptography now runs on them.
- Bell numbers How many ways can you split a set into groups? 1, 1, 2, 5, 15, 52, 203 — the counts of set partitions.
- Kaprekar numbers Square the number, cut the square in two, add the halves back together and get the number you started with — 45² = 2025 and 20 + 25 = 45.
- Automorphic numbers Numbers that reappear at the end of their own square: 5² = 25, 76² = 5776, 9376² = 87,909,376. They go on forever, one digit at a time.
- Vampire numbers Numbers that split into two equal-length factors built from their own digits — 1260 = 21 × 60. Clifford Pickover named them in 1994.
Random 13
- Bingo numbers Seeded ball draws for 75-ball and 90-ball bingo, with the B-I-N-G-O column letters where they apply.
- Coin flips Flip a fair — or deliberately weighted — coin as often as you like, with running counts and the longest streak.
- Dice rolls Roll any dice notation — 3d6, d20, 2d10+5 — and see every individual die alongside the total.
- Lottery number picker Reproducible random lines for Powerball, EuroMillions, UK Lotto, 6/49 and dozens of other real draw formats — with the honest caveat that no picker beats the odds.
- MongoDB-style ObjectIDs Twelve-byte, 24-hex-digit ObjectIDs with a real timestamp in the leading bytes — the identifier MongoDB puts in _id, in both its current and pre-3.4 layouts.
- Nano IDs Short URL-safe random IDs in the Nano ID style — 21 characters carry more entropy than a 36-character UUID.
- Normally distributed numbers Random values that cluster around a mean and thin out towards the tails — the bell curve, drawn by the Box–Muller transform.
- PIN codes Numeric PINs of 3 to 12 digits for test data and placeholders, with no-repeat and no-obvious-pattern options. Seeded, so not for real accounts.
- Raffle numbers Draw distinct winning tickets from any range, labelled by placing or by prize tier, from a seed you can share.
- Random integers Uniform whole numbers from any range, drawn from a seed — so the same link always produces the same list.
- UUIDs Reproducible UUID v4 and v7 in any quantity, in canonical, braced, URN or compact form — seeded, so a shared link always shows the same list.
- Weighted random numbers Draw from a list where some outcomes are deliberately more likely than others — loot tables, biased coins, traffic splits.
- Yes or no Ask a question and get a straight answer — yes, no, perhaps a maybe — or consult the twenty-answer oracle. Seeded, so the same question gets the same reply.
Test data 14
- EAN-13 barcodes Thirteen-digit retail barcode numbers with correct check digits, drawn from the GS1 prefixes that are never registered products.
- Fake phone numbers Dummy numbers drawn only from the blocks Ofcom, NANPA and the ACMA reserve for fiction — safe to print, safe to seed into a test database.
- IMEI numbers Structurally valid 15-digit IMEIs and 16-digit IMEISVs with a correct Luhn check digit, for test fixtures and QA — with an optional fixed Type Allocation Code.
- Invoice numbers Build invoice references from a pattern like INV-{YYYY}-{SEQ:5} — gapless, sequential and reproducible from the link.
- IP addresses Random IPv4 and IPv6 addresses from the ranges RFC 5737 and RFC 3849 reserve for documentation, so a copied example can never reach somebody’s real host.
- ISBN numbers Book numbers with correct check digits, in both the ten-digit form retired in 2007 and the thirteen-digit form that replaced it.
- MAC addresses Random EUI-48 addresses with the locally-administered bit set, so they cannot collide with a real vendor OUI — in colon, hyphen, Cisco dotted or bare form.
- Order numbers Build order references from a pattern, with an optional scramble that keeps them unique without making them consecutive.
- Postal codes Format-valid postal codes for 16 countries — for testing address forms and validation patterns, not for addressing mail.
- Serial numbers Build serial numbers from a pattern — date codes, look-alike-free characters and an optional Luhn check digit.
- SKU codes Build stock keeping units from a pattern — either a full category/size/colour matrix or a seeded random run.
- Test credit card numbers Luhn-valid card numbers built from the sandbox BINs that payment processors publish — for exercising checkout forms and test suites. Not real accounts.
- Test IBANs Structurally valid IBANs with correct ISO 7064 mod-97 check digits for seven European countries — format-valid test data, not real accounts.
- UPC-A barcodes Twelve-digit North American retail barcode numbers with correct check digits, defaulting to the number system reserved for in-store use.
Converters 9
- Binary numbers List a range of integers in base 2, with optional 0b prefix, nibble grouping and zero-padding to a fixed bit width.
- Fractions and decimals Convert fractions to decimals and back — exactly, including repeating decimals, with the fraction reduced to lowest terms.
- Hexadecimal numbers List a range of integers in base 16, with optional 0x prefix, byte-pair grouping and zero-padding to a fixed width.
- Number base converter Convert a number between any two bases from 2 to 36, with exact big-integer arithmetic and no precision loss.
- Numbers spelled out in words Spell any number out in words in eight languages, on either scale, with cheque wording and the British “and” as options.
- Ordinal numbers Ordinal numbers with the right ending in eight languages — including the 11th, 12th and 13th exception that catches most hand-written rules.
- Percentages Percent of a number, percent change, reverse percentages, and percentages as decimals and fractions — worked out exactly, line by line.
- Roman numerals Turn a number into Roman numerals, read a numeral back into digits, or print a whole range as a conversion chart.
- Scientific notation Convert between plain decimals, scientific notation, engineering notation and SI prefixes — with exact digit handling and significant-figure control.
Culture & curiosities 12
- Angel numbers What the New Age literature says 111, 444, 1111 and the other repeating sequences mean — attributed, dated and with no claim that any of it works.
- Benford law distribution Expected first- and second-digit frequencies under Benford’s law, plus a reproducible dataset that follows it exactly.
- Digital roots Add a number’s digits until one digit is left. The medieval arithmetic check behind casting out nines, in any base from 2 to 36.
- Facts about any number Enter a number and get everything provable about it — primality, factors, divisors, bases, Roman numerals — plus the real story behind the famous ones.
- Lucky and unlucky numbers Which numbers are treated as lucky or unlucky in China, Japan, Korea, Italy, Turkey, India and the West — and the entirely unrelated lucky numbers of Ulam's sieve.
- Named large numbers Million, billion, googol and beyond — including why a billion means two different things depending on where you are.
- Numerals in other writing systems Write the same number in Devanagari, Arabic-Indic, Chinese, Japanese, Roman, Greek, Hebrew, Thai, tally marks or Babylonian cuneiform.
- Numerology numbers Life path, expression and soul urge numbers worked out from a birth date and a name, with both the Pythagorean and Chaldean charts — presented as cultural history, not prediction.
- Palindrome dates Which days read the same backwards — worked out separately for DD/MM/YYYY, MM/DD/YYYY and YYYY-MM-DD, because palindromy is a property of notation rather than of time.
- Palindromic numbers Numbers that read the same in both directions — in base 10 or any base up to 36, optionally narrowed to primes, squares or cubes.
- Prime factorisation Split any whole number into its prime factors with exponents, using a 30-wheel trial division that works on big integers.
- Ulam spiral coordinates Winds the integers outward from a centre cell and marks the primes, drawing out the diagonal lines Stanisław Ulam spotted on graph paper in 1963.
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