Additive persistence: repeatedly sum digits until single digit. 9999→36→9. That's 2 steps. Digital root is the final value (9). Unlike multiplicative persistence (max 11), additive persistence is unbounded: use enough 9s for any desired persistence.
How to Use
Enter a number:
- Chain: Full sum sequence
- Persistence: Step count
- Digital root: Final value
Unbounded Growth
Want persistence k? Use 10^(10^(k-1)) - 1 (all 9s, enough of them). Digit sum of d nines = 9d. Need 9d to also have high persistence. So chain 999...9 → 9d → ... → single digit. Just use enough 9s!
Digital Root Shortcut
Digital root = 1 + (n-1) mod 9 (if n>0). This skips ALL intermediate steps! But persistence has no shortcut — you must actually iterate. The root is predictable; the step count requires computation.
Step-by-Step Instructions
- 1Enter number.
- 2Sum digits.
- 3Continue until single.
- 4Count steps.
- 5Note digital root.