Integer Sequences
This page is just a list of links to the various pages I have on certain categories of integer sequences.
Accelerating Sequences that "start out slow and speed up as they go along", and in a more interesting way than simply being faster than linear or faster than polynomial.
The Collatz 3X+1 iteration leads to several sequences.
Cullen and Woddall numbers and generalisations thereof.
Digits of Rational Fractions can be seen as sequences (of coefficients of powers of 10-n) which leads naturally to generating functions.
Dyadic operators (addition, multiplication, exponentiation, tetration, etc.)
Fermat numbers, and Prime Factors of Fermat Numbers
Floretions, a unique field reminiscent of sedenions, was used by their inventor to generate many sequences with unusual properties.
Kaprekar sequences depend entirely on being in base 10 but have some surprising patterns.
Linear recurrence sequences, i.e. 2nd-order recurrences, like the familiar Fibonacci numbers.
Mandelbrot set sequences (a few more on Mu-Ency).
The MCS Sequences, a broad class of recurrence relations.
The Narayana triangle and related.
My Software Related to Numbers and Sequences
RIES is a super-seeker for floating-point values, that returns results ordered by progressively better match and progressively greater complexity.
mcsfind is a super-seeker for integer sequences that explores the space of MCS definitions, and returns results ordered by progressively greater formula complexity.
Hypercalc, for those times when you want to work with really large quantities (e.g. "How many digits are there in 257885161-1?") but don't need to actually see all the digits. Hypercalc eats power-towers like 10101034 for lunch.
Sloandora is an experimental project to provide auto-recommendation browsing for the OEIS, based on a full substring-concordance metric.
If there is something else you were looking for, contact me (links below).
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2025 Apr 29.
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