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Omni-MATH / Let f:N→N be a function satisfying the following conditions: (a) f(1)=1 (b) f(a)≤f(b) whenever a and b are positive integers with a≤b. (c) f(2a)=f(a)+1 for all positive integers a.…

Problem

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problem

Let f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} be a function satisfying the following conditions: (a) f(1)=1f(1)=1 (b) f(a)≤f(b)f(a) \leq f(b) whenever aa and bb are positive integers with a≤ba \leq b. (c) f(2a)=f(a)+1f(2a)=f(a)+1 for all positive integers aa. How many possible values can the 2014-tuple (f(1),f(2),…,f(2014))(f(1), f(2), \ldots, f(2014)) take?
Plain-text mathematical notation (without MathML)
Let f:N→N be a function satisfying the following conditions: (a) f(1)=1 (b) f(a)≤f(b) whenever a and b are positive integers with a≤b. (c) f(2a)=f(a)+1 for all positive integers a. How many possible values can the 2014-tuple (f(1),f(2),…,f(2014)) take?
Original LaTeX notation
Let $f: \mathbb{N} \rightarrow \mathbb{N}$ be a function satisfying the following conditions: (a) $f(1)=1$ (b) $f(a) \leq f(b)$ whenever $a$ and $b$ are positive integers with $a \leq b$. (c) $f(2a)=f(a)+1$ for all positive integers $a$. How many possible values can the 2014-tuple $(f(1), f(2), \ldots, f(2014))$ take?

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Source and history

task_id
770c7436-7e5b-5746-9524-16b78b6b192d
task_key
test--770c7436-7e5b-5746-9524-16b78b6b192d
task_revision_id
1
config / split
/ test

Official source

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