Repdigit Numbers (Identical Digits)

Rule, exact count and rarity

A decimal repdigit repeats one digit throughout its entire written representation. For a digit d and a length k, its value is d × (10ᵏ − 1) / 9. Here d runs from 1 to 9 and the minimum length is two, so 11 qualifies but 1 does not. Leading zeros are never added. Every qualifying length contributes nine choices; the upper endpoint has mixed digits and does not qualify. Repdigits also read the same backwards, but their symmetry and repetition belong to different scoring families. A long string of equal digits is visually striking, yet length alone does not determine the final score.

The exact count, 45, 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 0.0045% 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(45 / 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 55, with a rarity score of 1,377 and Top 0.0006%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.

Complete list of repdigits

The highest-scoring match

The highest-scoring representative is 55, with a rarity score of 1,377 and Top 0.0006%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.