Patterns /Number Theory
Powers of Two
Each power of two is double the last: 1, 2, 4, 8, 16, and on up through 1024, 65536 and 524288. Doubling exhausts the range in only twenty steps.
Exponential growth means the count is logarithmic in the range — extending the site to ten million would add just three more. That is about as scarce as a trait can get while still having members at every scale.
Powers of two are the most culturally recognisable numbers in computing: 256, 1024, 4096 and 65536 all appear as limits, buffer sizes and colour depths, which is why they get looked up far more often than their count would suggest.
Every power of two above 1 is also a binary repdigit of sorts — a single 1 followed by zeros — so these numbers usually pick up representation traits as well.
Highest-scoring examples
The best-scoring numbers of four digits or more that carry this pattern. Shorter numbers are excluded here because their length alone dominates any score ranking.
Smallest examples
The first numbers in the range that match this pattern.
Related number theory patterns
Prime Numbers
A prime has no divisors other than 1 and itself. They are the building blocks every other number is assembled from.
Semiprime Numbers
A semiprime is a product of exactly two primes, counted with multiplicity — 15 = 3 × 5, and 49 = 7 × 7 counts too.
Perfect Squares
A perfect square is some whole number times itself: 144 = 12², 10000 = 100². The range ends neatly on 1,000,000 = 1000².
Perfect Cubes
A perfect cube is a whole number raised to the third power: 216 = 6³, 970299 = 99³. There are only about a hundred in the entire range.
Fibonacci Numbers
Each Fibonacci number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13 … reaching 832040 before the range runs out.