A number theory problem by Pi Han Goh

Number Theory Level 4

an=an−1+gcd⁡(n,an−1) \large a_n = a_{n-1} + \gcd(n,a_{n-1})

Consider the recurrence relation above with for n≥2n\geq2 with a1=7a_1 = 7. And define bn=an+1−anb_n= a_{n+1} - a_n , find the number of composite numbers bnb_n for n≤109n\leq10^9 .

For the sake of this question, take 1 as neither prime nor composite.

Pi Han Goh by Pi Han Goh
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