Pattern guide
Prime & Modular Anomaly
Terms are prime numbers, perfect squares, Fibonacci numbers, or follow a clock-like modular rule.
When none of the other four patterns fit, look for a hidden mathematical property: are the terms all prime? All perfect squares? Following the Fibonacci rule? Or cycling through a fixed range (modular arithmetic)? These sequences do not follow a simple additive or multiplicative rule — they follow a membership rule.
How to recognise it
- 1Try differences and ratios first — if both fail, switch to property checking.
- 2Test for primes: 2, 3, 5, 7, 11, 13, 17, 19, 23...
- 3Test for perfect squares: 1, 4, 9, 16, 25, 36, 49...
- 4Test for Fibonacci: each term = sum of the two before it (1, 1, 2, 3, 5, 8, 13, 21...).
- 5Test for modular cycling: if terms cycle back (e.g. 1, 3, 2, 4, 1, 3, 2, 4), the sequence repeats with a fixed period.
Worked examples
Example 1
2
3
5
7
11
13
?
Rule: Consecutive prime numbers
2 → 3(both prime)
3 → 5(both prime (4 is skipped, not prime))
5 → 7(both prime (6 is skipped))
7 → 11(both prime (8, 9, 10 skipped))
11 → 13(both prime (12 skipped))
13 → ?(next prime after 13 is 17)
Answer: Next prime: 17
Example 2
1
4
9
16
25
?
Rule: Perfect squares: 1², 2², 3², 4², 5², 6²
1 → 4(1² = 1, 2² = 4)
4 → 9(3² = 9)
9 → 16(4² = 16)
16 → 25(5² = 25)
25 → ?(6² = 36)
Answer: 6² = 36
Example 3
1
1
2
3
5
8
13
?
Rule: Fibonacci: each term = sum of the two before it
1 + 1 → 2
1 + 2 → 3
2 + 3 → 5
3 + 5 → 8
5 + 8 → 13
8 + 13 → ?(8 + 13 = 21)
Answer: 8 + 13 = 21
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