{"schema":"vela.problem-packet.v0.1","problem":236,"statement":"Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\\geq 0$. Is it true that $f(n)=o(\\log n)$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A039669","name":"Numbers n > 2 such that n - 2^k is a prime for all k > 0 with 2^k < n.","terms":"4,7,15,21,45,75,105","url":"https://oeis.org/A039669"},{"id":"A109925","name":"Number of primes of the form n - 2^k.","terms":"0,0,1,2,1,2,2,1,2,1,2,1,2,1,3,0,1,2,3,1,4,0,2,1,2,0,3,0,1,1,2,1,3,1,3,0,2,1,4,0,1,1,2,1,5,0,2,1,3,0,3,0,1,1,3,0,2,0,1,1,","url":"https://oeis.org/A109925"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}