integer-sequences

Functional library for precise access to integer sequences such as prime numbers, square numbers, triangle numbers, etc

Intro

npm install --save integer-sequences

Functional library for precise access to integer sequences. Total unit test coverage. Cached access offers performance. For example:

const intseqs = require('integer-sequences')
intseqs.prime.sequenceMax(100000000)  // takes 1900ms - first call
intseqs.prime.sequenceMax(100000000)  // takes 25ms - second cached call

It makes use of Big.js to guarantee precision when working with big numbers.

Numeric arguments can be given as:

• strings - e.g. intseqs.prime.isTerm('1000000')
• Big.js objects - e.g. intseqs.prime.isTerm(Big('1000000')) or intseqs.prime.isTerm(Big(1000000))
• numbers - e.g. intseqs.prime.isTerm(1000000)

Function return values are typically Big.js objects. To access a Big.js object value:

const intseqs = require('integer-sequences')
const bigObj = intseqs.prime.term(10)
const value = bigObj.toFixed()
console.log(value) // logs '29'

Misc functions

intseqs.getNumbersAsJson(max: number)  // Returns a list of numeric JSON objects

Example:

intseqs.getNumbersAsJson(7)

Returns:

[
  {number: 1, cube: Big(1), fibonacci: [Big(1), Big(2)], padovan: [Big(1), Big(2), Big(3)], prime: false, tetrahedron: Big(1), triangle: Big(1), square: Big(1)},
  {number: 2, cube: false, fibonacci: Big(3), padovan: [Big(4), Big(5)], prime: 1, tetrahedron: false, triangle: false, square: false},
  {number: 3, cube: false, fibonacci: Big(4), padovan: Big(6), prime: 2, tetrahedron: false, triangle: Big(2), square: false},
  {number: 4, cube: false, fibonacci: false, padovan: Big(7), prime: false, tetrahedron: Big(2), triangle: false, square: Big(2)},
  {number: 5, cube: false, fibonacci: Big(5), padovan: Big(8), prime: 3, tetrahedron: false, triangle: false, square: false},
  {number: 6, cube: false, fibonacci: false, padovan: false, prime: false, tetrahedron: false, triangle: Big(3), square: false},
  {number: 7, cube: false, fibonacci: false, padovan: Big(9), prime: 4, tetrahedron: false, triangle: false, square: false}
]

Prime values returned may be of type number for performance reasons.

intseqs.getNumberAsJson(n: number)  // Returns the nth numeric JSON object

Prime numbers - A000040

term - isTerm - isTermFast

Full support for primes upto Prime(6000000)=104395301 (partial support thereafter)

intseqs.prime.sequence(n: number)       // Returns a list of the first n terms in the sequence
intseqs.prime.sequenceMax(max: number)  // Returns a list of the first terms, all terms being <= max
intseqs.prime.term(n: number)           // Returns the nth term
intseqs.prime.isTerm(n: number)         // Returns x where n is the xth term or false where n is not a term
intseqs.prime.isTermFast(n: number)     // Returns a boolean, is n a term?

Cube numbers - A000578

term isTerm

intseqs.cube.sequence(n: number)
intseqs.cube.sequenceMax(max: number)
intseqs.cube.term(n: number)
intseqs.cube.isTerm(n: number)

Fibonacci numbers - A000045

term isTerm isTermFast

intseqs.fibonacci.sequence(n: number)
intseqs.fibonacci.sequenceMax(max: number)
intseqs.fibonacci.term(n: number)
intseqs.fibonacci.isTerm(n: number)
intseqs.fibonacci.isTermFast(n: number)

Padovan numbers - A134816

term isTerm

intseqs.padovan.sequence(n: number)
intseqs.padovan.sequenceMax(max: number)
intseqs.padovan.term(n: number)
intseqs.padovan.isTerm(n: number)

Square numbers - A000290

term isTerm

intseqs.square.sequence(n: number)
intseqs.square.sequenceMax(max: number)
intseqs.square.term(n: number)
intseqs.square.isTerm(n: number)

Tetrahedron numbers - A000292

term isTerm

intseqs.tetrahedron.sequence(n: number)
intseqs.tetrahedron.sequenceMax(max: number)
intseqs.tetrahedron.term(n: number)
intseqs.tetrahedron.isTerm(n: number)

Triangle numbers - A000217

term isTerm

intseqs.triangle.sequence(n: number)
intseqs.triangle.sequenceMax(max: number)
intseqs.triangle.term(n: number)
intseqs.triangle.isTerm(n: number)

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