Happy Numbers
Numbers that eventually reach joy (the number 1).
What is it?
Take a number, square each digit, add the squares, and repeat. If you eventually reach 1, the number is happy. 19 is happy: 1²+9²=82, 8²+2²=68, 6²+8²=100, 1²+0²+0²=1. Unhappy numbers loop forever through 4 instead.
- Exact matches143,071
- Odds1 in 7
- Out of1,000,001
How it scores
Happy numbers make up roughly one in seven of the range, so the trait scores modestly — but it is one of the most delightful facts a daily roll can carry.
The formula: -log2(count / 1,000,001) bits per trait, capped at 20, summed with 0.5 decay per additional trait.
Highest-scoring happy numbers
- 1,000,000score 34.5 · Mythic
- 1score 31.3 · Mythic
- 1,000score 27.7 · Mythic
- 100,000score 27.1 · Mythic
- 10,000score 26.3 · Mythic
- 899,999score 26.1 · Mythic
- 999,998score 25.9 · Mythic
- 4,096score 25.7 · Mythic
- 9,001score 25.4 · Mythic
- 100score 24.7 · Mythic
Related patterns
FAQ
Is 1 a happy number?
Yes, trivially — it is already at 1, the destination.
What makes a number unhappy?
Unhappy numbers fall into the cycle 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 and never escape.
Are there happy primes?
Yes — they are called happy primes, and 7 is the smallest. A roll that is both prime and happy stacks both traits.