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Omni-MATH / Let the sequence a_(i) be defined as a_(i+1)=2^(a_(i)). Find the number of integers 1≤n≤1000 such that if a₀=n, then 100 divides a₁₀₀₀−a₁.

Problem

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problem

Let the sequence aia_{i} be defined as ai+1=2aia_{i+1}=2^{a_{i}}. Find the number of integers 1≤n≤10001 \leq n \leq 1000 such that if a0=na_{0}=n, then 100 divides a1000−a1a_{1000}-a_{1}.
Plain-text mathematical notation (without MathML)
Let the sequence a_(i) be defined as a_(i+1)=2^(a_(i)). Find the number of integers 1≤n≤1000 such that if a₀=n, then 100 divides a₁₀₀₀−a₁.
Original LaTeX notation
Let the sequence $a_{i}$ be defined as $a_{i+1}=2^{a_{i}}$. Find the number of integers $1 \leq n \leq 1000$ such that if $a_{0}=n$, then 100 divides $a_{1000}-a_{1}$.

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Source and history

task_id
53a63d79-c8a2-5c9e-8c51-99d622be3c79
task_key
test--53a63d79-c8a2-5c9e-8c51-99d622be3c79
task_revision_id
1
config / split
/ test

Official source

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