|
Math::NumSeq
|
number sequences
|
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60 |
|
Math::NumSeq::Abundant
|
abundant numbers, greater than sum of divisors
|
|
60 |
|
Math::NumSeq::AlgebraicContinued
|
continued fraction expansion of algebraic numbers
|
|
60 |
|
Math::NumSeq::All
|
all integers
|
|
60 |
|
Math::NumSeq::AllDigits
|
digits of the integers
|
|
60 |
|
Math::NumSeq::AllPrimeFactors
|
prime factors of the integers
|
|
60 |
|
Math::NumSeq::AlmostPrimes
|
semiprimes and other fixed number of prime factors
|
|
60 |
|
Math::NumSeq::AsciiSelf
|
sequence is its own ASCII digits
|
|
60 |
|
Math::NumSeq::BalancedBinary
|
balanced 1,0 bits
|
|
60 |
|
Math::NumSeq::Base::Array
|
|
|
60 |
|
Math::NumSeq::Base::Cache
|
|
|
60 |
|
Math::NumSeq::Base::Digits
|
|
|
60 |
|
Math::NumSeq::Base::IterateIth
|
iterate by calling ith() successively
|
|
60 |
|
Math::NumSeq::Base::IteratePred
|
iterate by searching with pred()
|
|
60 |
|
Math::NumSeq::Base::Sparse
|
|
|
60 |
|
Math::NumSeq::BaumSweet
|
Baum-Sweet sequence
|
|
60 |
|
Math::NumSeq::Beastly
|
numbers containing digits "666"
|
|
60 |
|
Math::NumSeq::Catalan
|
Catalan numbers (2n)! / (n!*(n+1)!)
|
|
60 |
|
Math::NumSeq::CollatzSteps
|
steps in the "3n+1" problem
|
|
60 |
|
Math::NumSeq::ConcatNumbers
|
concatenate digits of i, i+1
|
|
60 |
|
Math::NumSeq::Cubes
|
cubes i**3
|
|
60 |
|
Math::NumSeq::CullenNumbers
|
Cullen numbers i*2^i+1
|
|
60 |
|
Math::NumSeq::DedekindPsiCumulative
|
cumulative Psi function
|
|
60 |
|
Math::NumSeq::DedekindPsiSteps
|
psi function until 2^x*3^y
|
|
60 |
|
Math::NumSeq::DeletablePrimes
|
primes deleting a digit repeatedly
|
|
60 |
|
Math::NumSeq::DigitCount
|
count of a given digit
|
|
60 |
|
Math::NumSeq::DigitCountHigh
|
count of given high digits
|
|
60 |
|
Math::NumSeq::DigitCountLow
|
count of given low digits
|
|
60 |
|
Math::NumSeq::DigitLength
|
length in digits
|
|
60 |
|
Math::NumSeq::DigitLengthCumulative
|
total length in digits of numbers 1 to i
|
|
60 |
|
Math::NumSeq::DigitProduct
|
product of digits
|
|
60 |
|
Math::NumSeq::DigitProductSteps
|
multiplicative persistence and digital root
|
|
60 |
|
Math::NumSeq::DigitSum
|
sum of digits, possibly with powering
|
|
60 |
|
Math::NumSeq::DigitSumModulo
|
digit sum taken modulo a given modulus
|
|
60 |
|
Math::NumSeq::DivisorCount
|
how many divisors
|
|
60 |
|
Math::NumSeq::DuffinianNumbers
|
no common factor with sum of divisors
|
|
60 |
|
Math::NumSeq::Emirps
|
primes backwards and forwards
|
|
60 |
|
Math::NumSeq::ErdosSelfridgeClass
|
Erdos-Selfridge classification of primes
|
|
60 |
|
Math::NumSeq::Even
|
even integers
|
|
60 |
|
Math::NumSeq::Expression
|
mathematical expression values
|
|
60 |
|
Math::NumSeq::Factorials
|
factorials i! = 1*2*...*i
|
|
60 |
|
Math::NumSeq::Fibbinary
|
without consecutive 1-bits
|
|
60 |
|
Math::NumSeq::FibbinaryBitCount
|
number of bits in each fibbinary number
|
|
60 |
|
Math::NumSeq::Fibonacci
|
Fibonacci numbers
|
|
60 |
|
Math::NumSeq::FibonacciWord
|
0/1 related to Fibonacci numbers
|
|
60 |
|
Math::NumSeq::File
|
sequence read from a file
|
|
60 |
|
Math::NumSeq::FractionDigits
|
the digits of a fraction p/q
|
|
60 |
|
Math::NumSeq::GolayRudinShapiro
|
parity of adjacent 11 bit pairs
|
|
60 |
|
Math::NumSeq::GolayRudinShapiroCumulative
|
cumulative Golay/RudinShapiro sequence
|
|
60 |
|
Math::NumSeq::GoldbachCount
|
number of representations as sum of primes P+Q
|
|
60 |
|
Math::NumSeq::GolombSequence
|
sequence is its own run lengths, 1 upwards
|
|
60 |
|
Math::NumSeq::HappyNumbers
|
reaching 1 under repeated sum of squares of digits
|
|
60 |
|
Math::NumSeq::HappySteps
|
number of sum of squares of digits iterations to reach a repeat
|
|
60 |
|
Math::NumSeq::HarshadNumbers
|
numbers divisible by sum of digits
|
|
60 |
|
Math::NumSeq::HofstadterFigure
|
sequence excludes its own first differences
|
|
60 |
|
Math::NumSeq::JugglerSteps
|
steps in the juggler sqrt sequence
|
|
60 |
|
Math::NumSeq::KlarnerRado
|
Klarner-Rado sequences
|
|
60 |
|
Math::NumSeq::Kolakoski
|
sequence of 1s and 2s its own run lengths
|
|
60 |
|
Math::NumSeq::LemoineCount
|
number of representations as P+2*Q for primes P,Q
|
|
60 |
|
Math::NumSeq::LiouvilleFunction
|
Liouville function sequence
|
|
60 |
|
Math::NumSeq::LucasNumbers
|
Lucas numbers
|
|
60 |
|
Math::NumSeq::LuckyNumbers
|
sieved out multiples by the sequence itself
|
|
60 |
|
Math::NumSeq::MaxDigitCount
|
maximum count of a given digit in any radix
|
|
60 |
|
Math::NumSeq::MephistoWaltz
|
Mephisto waltz sequence
|
|
60 |
|
Math::NumSeq::MobiusFunction
|
Mobius function sequence
|
|
60 |
|
Math::NumSeq::Modulo
|
remainders modulo of a given number
|
|
60 |
|
Math::NumSeq::MoranNumbers
|
numbers divided by sum of digits giving a prime
|
|
60 |
|
Math::NumSeq::Multiples
|
multiples of a given number
|
|
60 |
|
Math::NumSeq::NumAronson
|
numerical version of Aronson's sequence
|
|
60 |
|
Math::NumSeq::OEIS
|
number sequence by OEIS A-number
|
|
60 |
|
Math::NumSeq::OEIS::Catalogue
|
available A-numbers
|
|
60 |
|
Math::NumSeq::OEIS::Catalogue::Plugin
|
pluggable catalogue extensions
|
|
60 |
|
Math::NumSeq::OEIS::Catalogue::Plugin::BuiltinTable
|
|
|
60 |
|
Math::NumSeq::OEIS::Catalogue::Plugin::FractionDigits
|
|
|
60 |
|
Math::NumSeq::OEIS::Catalogue::Plugin::ZZ_Files
|
|
|
60 |
|
Math::NumSeq::OEIS::File
|
|
|
60 |
|
Math::NumSeq::Odd
|
odd integers
|
|
60 |
|
Math::NumSeq::Palindromes
|
palindrome numbers like 15351
|
|
60 |
|
Math::NumSeq::Pell
|
Pell numbers
|
|
60 |
|
Math::NumSeq::Perrin
|
Perrin sequence
|
|
60 |
|
Math::NumSeq::PisanoPeriod
|
cycle length of Fibonacci numbers mod i
|
|
60 |
|
Math::NumSeq::PisanoPeriodSteps
|
Fibonacci frequency and Leonardo logarithm
|
|
60 |
|
Math::NumSeq::PolignacObstinate
|
odd integers not prime+2^k
|
|
60 |
|
Math::NumSeq::Polygonal
|
polygonal numbers, triangular, square, pentagonal, etc
|
|
60 |
|
Math::NumSeq::PowerFlip
|
prime exponent flip
|
|
60 |
|
Math::NumSeq::PowerPart
|
largest square root etc divisor
|
|
60 |
|
Math::NumSeq::Powerful
|
numbers with certain prime powers
|
|
60 |
|
Math::NumSeq::PrimeFactorCount
|
how many prime factors
|
|
60 |
|
Math::NumSeq::PrimeIndexOrder
|
order of primeness by primes at prime indexes
|
|
60 |
|
Math::NumSeq::PrimeIndexPrimes
|
primes with prime number indexes
|
|
60 |
|
Math::NumSeq::Primes
|
prime numbers
|
|
60 |
|
Math::NumSeq::Primorials
|
primorials 2*3*...*p[i]
|
|
60 |
|
Math::NumSeq::Pronic
|
pronic numbers
|
|
60 |
|
Math::NumSeq::ProthNumbers
|
Proth number sequence
|
|
60 |
|
Math::NumSeq::PythagoreanHypots
|
hypotenuses of Pythagorean triples
|
|
60 |
|
Math::NumSeq::RadixConversion
|
radix conversion
|
|
60 |
|
Math::NumSeq::RadixWithoutDigit
|
integers without a given digit
|
|
60 |
|
Math::NumSeq::ReReplace
|
sequence of repeated replacements
|
|
60 |
|
Math::NumSeq::ReRound
|
sequence from repeated rounding up
|
|
60 |
|
Math::NumSeq::RepdigitAny
|
numbers which are a repdigit in any radix
|
|
60 |
|
Math::NumSeq::RepdigitRadix
|
radix in which i is a repdigit
|
|
60 |
|
Math::NumSeq::Repdigits
|
repdigits 11, 22, 33, etc
|
|
60 |
|
Math::NumSeq::ReverseAdd
|
steps of the reverse-add algorithm
|
|
60 |
|
Math::NumSeq::ReverseAddSteps
|
steps of the reverse-add algorithm to reach palindrome
|
|
60 |
|
Math::NumSeq::Runs
|
runs of consecutive integers
|
|
60 |
|
Math::NumSeq::SelfLengthCumulative
|
cumulative digit length of own values
|
|
60 |
|
Math::NumSeq::SophieGermainPrimes
|
Sophie Germain primes p and 2*p+1 prime
|
|
60 |
|
Math::NumSeq::SpiroFibonacci
|
recurrence around a square spiral
|
|
60 |
|
Math::NumSeq::SqrtContinued
|
continued fraction expansion of a square root
|
|
60 |
|
Math::NumSeq::SqrtContinuedPeriod
|
period of the continued fraction for sqrt(i)
|
|
60 |
|
Math::NumSeq::SqrtDigits
|
the digits of a square root
|
|
60 |
|
Math::NumSeq::SqrtEngel
|
Engel expansion of a square root
|
|
60 |
|
Math::NumSeq::Squares
|
perfect squares
|
|
60 |
|
Math::NumSeq::StarNumbers
|
star numbers 6*i*(i-1)+1
|
|
60 |
|
Math::NumSeq::SternDiatomic
|
Stern's diatomic sequence
|
|
60 |
|
Math::NumSeq::Tetrahedral
|
tetrahedral numbers i*(i+1)*(i+2)/6
|
|
60 |
|
Math::NumSeq::Totient
|
Euler's totient function, count of coprimes
|
|
60 |
|
Math::NumSeq::TotientCumulative
|
cumulative totients
|
|
60 |
|
Math::NumSeq::TotientPerfect
|
sum of repeated totients is N itself
|
|
60 |
|
Math::NumSeq::TotientSteps
|
count of repeated totients to reach 1
|
|
60 |
|
Math::NumSeq::TotientStepsSum
|
sum of repeated totients to reach 1
|
|
60 |
|
Math::NumSeq::Triangular
|
triangular numbers
|
|
60 |
|
Math::NumSeq::Tribonacci
|
Tribonacci numbers
|
|
60 |
|
Math::NumSeq::TwinPrimes
|
twin primes
|
|
60 |
|
Math::NumSeq::UlamSequence
|
integers uniquely the sum of two previous terms
|
|
60 |
|
Math::NumSeq::UndulatingNumbers
|
numbers with alternating digits ABABAB...
|
|
60 |
|
Math::NumSeq::WoodallNumbers
|
Woodall numbers i*2^i-1
|
|
60 |
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