Number theory · Primes · Prime gaps · Modular arithmetic
Consider strictly increasing sequences \(a_1, a_2, a_3, \dots\) of prime numbers in which any two consecutive terms differ by \(2\) or by \(4\); that is,
\[ a_{i+1} - a_i \in \{2, 4\} \quad \text{for every } i. \]
Determine the greatest possible number of terms such a sequence can have.
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Serbian Municipal Competition 2016, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source