Computed with engine art-1.0.0. Data updated: 2026-09-26 (UTC). Rules independently implemented by RNGDLE.ART.
Sequences
Rule, exact count and rarity
A zigzag number has at least four decimal digits whose adjacent comparisons strictly alternate between rising and falling. Either direction may come first. Step sizes do not need to match or equal one: only the alternating signs matter. Equal neighbors break the pattern because every comparison must be strict. This is a descriptive shape rule on the decimal representation, not a requirement that the digits form a permutation of consecutive integers. Repeated digits can still occur at nonadjacent positions. Some two-symbol alternating numbers also zigzag, while other zigzags use many different symbols. The test records a single whole-number pattern and does not award extra matches for each peak or trough inside the representation.
The exact count, 136,425, comes from evaluating all 1,000,001 integers from 0 through 1,000,000, including both endpoints. It is not a sample or an estimate. Each matching integer is counted once for this category, even if it contains multiple qualifying segments. Its frequency of 13.642486% describes the chance that a uniformly chosen integer passes this one test. It is not the global score percentile of every member, and overlapping pattern counts must not be added as if they represented disjoint sets.
The pattern supplies −log₂(136,425 / 1,000,001) bits before its within-family weight is applied. Other matched patterns, digit sum, distinct-digit count and short-length signals can change the complete score. Consequently, members of this category need not share a ranking. The highest-scoring representative is 5,050, with a rarity score of 1,017 and Top 0.0034%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Example numbers
ExploreThe highest-scoring match
The highest-scoring representative is 5,050, with a rarity score of 1,017 and Top 0.0034%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Frequently asked questions
How many zigzag digit numbers are there between 0 and 1,000,000?
There are exactly 136,425 matches for zigzag digit numbers among the 1,000,001 integers from 0 to 1,000,000, inclusive: 13.642486% of the range. At least four digits strictly alternate between rising and falling.
Do equal adjacent digits count as a zigzag turn?
No. Every adjacent comparison must be strictly up or down. Equal neighbors make the zigzag test fail.
What is the highest-scoring zigzag digit numbers representative?
The highest-scoring representative is 5,050, with a rarity score of 1,017 and Top 0.0034%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.