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Omni-MATH / A set of positive integers is called [i]fragrant[/i] if it contains at least two…

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problem

A set of positive integers is called [i]fragrant[/i] if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements. Let P(n)=n2+n+1P(n)=n^2+n+1. What is the least possible positive integer value of bb such that there exists a non-negative integer aa for which the set {P(a+1),P(a+2),…,P(a+b)}\{P(a+1),P(a+2),\ldots,P(a+b)\} is fragrant?
Plain-text mathematical notation (without MathML)
A set of positive integers is called [i]fragrant[/i] if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements.  Let P(n)=n²+n+1.  What is the least possible positive integer value of b such that there exists a non-negative integer a for which the set {P(a+1),P(a+2),…,P(a+b)} is fragrant?
Original LaTeX notation
A set of positive integers is called [i]fragrant[/i] if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements.  Let $P(n)=n^2+n+1$.  What is the least possible positive integer value of $b$ such that there exists a non-negative integer $a$ for which the set $$\{P(a+1),P(a+2),\ldots,P(a+b)\}$$ is fragrant?

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Source and history

task_id
7ddff69a-7c5b-5af8-8cae-a97750e2e4ec
task_key
test--7ddff69a-7c5b-5af8-8cae-a97750e2e4ec
task_revision_id
1
config / split
/ test

Official source

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