Patterns /Sequences
ABAB Pattern Numbers
Two digits taking strict turns: 5252, 8080, 393939. The pattern repeats with period two from the first digit to the last.
How long might abab pattern numbers take?
1 in 4,115.2 per roll · 4,115 rolls on average.
At one daily specimen a day, the mean is about 11.3 years. A 50% chance takes 2,853 rolls; 90% takes 9,475.
7 daily rolls
1 in 588
30 daily rolls
1 in 138
365 daily rolls
8.49%
1 in 138 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.
An ABAB number is fully specified by two digits, no matter how long it is — which is why the count above stays flat while the range grows by a factor of ten at each length.
Alternation is a stronger constraint than merely using two distinct digits. 5522 uses the same two digits but has no period-two structure, so it does not qualify here.
Even-length ABAB numbers are often palindromic-adjacent but not palindromes, which makes them a good illustration of why symmetry and sequence are scored as separate groups.
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 sequences patterns
Ascending Sequence Numbers
Every digit is exactly one higher than the one before it: 123, 4567, 456789. There are only a few dozen such numbers in the entire range.
Descending Sequence Numbers
Each digit is exactly one lower than the previous: 321, 6543, 987654. The mirror image of an ascending sequence, and just as scarce.
Ascending Digit Runs
A partial climb: somewhere in the number sit three or more digits each one higher than the last, as in the 456 inside 74560.
Descending Digit Runs
Three or more digits each one lower than the last, appearing anywhere in the number — the 543 inside 15432, for instance.
ABCABC Pattern Numbers
A three-digit block written twice: 146146, 707707, 989989. Every six-digit number of this form is a three-digit number multiplied by 1001.