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Omni-MATH / For an integer x≥1, let p(x) be the least prime that does not divide x, and define q(x) to be the product of all primes less than p(x). In particular, p(1)=2. For x having p(x)=2, …

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For an integer x≥1x \geq 1, let p(x)p(x) be the least prime that does not divide xx, and define q(x)q(x) to be the product of all primes less than p(x)p(x). In particular, p(1)=2.p(1) = 2. For xx having p(x)=2p(x) = 2, define q(x)=1q(x) = 1. Consider the sequence x0,x1,x2,…x_0, x_1, x_2, \ldots defined by x0=1x_0 = 1 and xn+1=xnp(xn)q(xn) x_{n+1} = \frac{x_n p(x_n)}{q(x_n)} for n≥0n \geq 0. Find all nn such that xn=1995x_n = 1995.
Plain-text mathematical notation (without MathML)
For an integer x≥1, let p(x) be the least prime that does not divide x, and define q(x) to be the product of all primes less than p(x). In particular, p(1)=2. For x having p(x)=2, define q(x)=1. Consider the sequence x₀,x₁,x₂,… defined by x₀=1 and x_(n+1)=(x_(n)p(x_(n)))/(q(x_(n))) for n≥0. Find all n such that x_(n)=1995.
Original LaTeX notation
For an integer $x \geq 1$, let $p(x)$ be the least prime that does not divide $x$, and define $q(x)$ to be the product of all primes less than $p(x)$. In particular, $p(1) = 2.$ For $x$ having $p(x) = 2$, define $q(x) = 1$. Consider the sequence $x_0, x_1, x_2, \ldots$ defined by $x_0 = 1$ and \[ x_{n+1} = \frac{x_n p(x_n)}{q(x_n)} \] for $n \geq 0$. Find all $n$ such that $x_n = 1995$.

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task_id
f602207f-b77b-5eac-95d9-5f76e911f2d5
task_key
test--f602207f-b77b-5eac-95d9-5f76e911f2d5
task_revision_id
1
config / split
/ test

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