A field guide to extraordinary numbers.
Explore every pattern and collect a personal record through daily specimens.
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Manual analysis and ordinary rolls do not stamp the atlas. Only daily specimens do.
Repdigit number
At least two digits, all identical.
At least five repeated digits
One digit appears five or more times; not a full repdigit.
Exactly four repeated digits
The most frequent digit appears exactly four times; not all digits are identical.
Exactly three repeated digits
The most frequent digit appears exactly three times; not all digits are identical.
Multiple digit pairs
At least two pairs, with no digit appearing more than twice.
Exactly one digit pair
Exactly one pair; every other digit appears once. Two-digit repdigits are excluded.
Consecutive repeated digits
At least three identical digits next to one another; not a full repdigit.
Exactly two distinct digits
Four or more places use exactly two different digits.
Palindrome number
Two or more digits read the same in either direction.
Consecutive ascending digits
At least three digits; each rises by exactly one.
Consecutive descending digits
At least three digits; each falls by exactly one.
Ascending segment
A segment of at least three digits climbs by one; the full number is not a sequence.
Descending segment
A segment of at least three digits falls by one; the full number is not a sequence.
ABAB pattern
At least four places alternate between two distinct digits.
ABCABC pattern
A three-digit block repeats twice, using at least two distinct digits.
Alternating parity
At least four digits alternate between odd and even.
Zigzag digits
At least four digits strictly alternate between rising and falling.
Harshad number
A positive number divisible by the sum of its digits.
Happy number
Repeatedly summing squared digits eventually reaches 1.
Prime number
A number greater than 1 with exactly two positive divisors.
Semiprime
A product of two primes, which may be equal.
Perfect square
The square of a nonnegative integer, including 0 and 1.
Perfect cube
The cube of a nonnegative integer, including 0 and 1.
Power of two
2 raised to a nonnegative integer power, including 1.
Fibonacci number
A member of the Fibonacci sequence: 0, 1, 2, 3, 5, 8…
Triangular number
A sum of consecutive integers starting at 1, with 0 included.
Factorial
A product 1 × 2 × … × k, including 1.
At least 100 positive divisors
At least 100 distinct positive divisors.
Binary palindrome
At least two binary digits read the same in reverse.
Mersenne number (binary repunit)
The binary representation has at least two digits, all 1.
Hexadecimal repdigit
At least two identical digits in hexadecimal notation.