Patterns /Number Theory
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.
How long might fibonacci numbers take?
1 in 33,333.4 per roll · 33,333 rolls on average.
At one daily specimen a day, the mean is about 91.3 years. A 50% chance takes 23,105 rolls; 90% takes 76,752.
7 daily rolls
1 in 4,762
30 daily rolls
1 in 1,112
365 daily rolls
1.09%
1 in 1,112 chance of at least one match in 30 independent rolls.
Waiting times are averages, not deadlines. Previous misses do not increase the next roll’s chance. Only Daily Specimens stamp your Atlas.
The sequence grows geometrically, by a factor of about 1.618 each step, so like powers of two it exhausts a million in a few dozen terms. The exact count in range is shown above.
That growth ratio is the golden ratio, which is why Fibonacci numbers keep turning up in geometry, plant growth and design — the sequence is the integer shadow of a constant that appears everywhere.
Fibonacci membership is invisible from a number's digits, so it is one of the traits that most often surprises players when a plain-looking number turns out to score 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.
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.