A number theory problem by Pi Han Goh

an=an1+gcd(n,an1) \large a_n = a_{n-1} + \gcd(n,a_{n-1})

Consider the recurrence relation above with for n2n\geq2 with a1=7a_1 = 7. And define bn=an+1anb_n= a_{n+1} - a_n , find the number of composite numbers bnb_n for n109n\leq10^9 .

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

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