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Omni-MATH / For any positive integer n, let f(n) denote the number of 1's in the base-2 representation of n. For how many values of n with 1≤n≤2002 do we have f(n)=f(n+1)?

Problem

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problem

For any positive integer nn, let f(n)f(n) denote the number of 1's in the base-2 representation of nn. For how many values of nn with 1≤n≤20021 \leq n \leq 2002 do we have f(n)=f(n+1)f(n)=f(n+1)?
Plain-text mathematical notation (without MathML)
For any positive integer n, let f(n) denote the number of 1's in the base-2 representation of n. For how many values of n with 1≤n≤2002 do we have f(n)=f(n+1)?
Original LaTeX notation
For any positive integer $n$, let $f(n)$ denote the number of 1's in the base-2 representation of $n$. For how many values of $n$ with $1 \leq n \leq 2002$ do we have $f(n)=f(n+1)$?

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Source and history

task_id
a4359773-a7f6-5dff-86c4-6badf97fa2cc
task_key
test--a4359773-a7f6-5dff-86c4-6badf97fa2cc
task_revision_id
1
config / split
/ test

Official source

initial import