{"schema":"vela.problem-packet.v0.1","problem":1135,"statement":"Define $f:\\mathbb{N}\\to \\mathbb{N}$ by $f(n)=n/2$ if $n$ is even and $f(n)=\\frac{3n+1}{2}$ if $n$ is odd.Given any integer $m\\geq 1$ does there exist $k\\geq 1$ such that $f^{(k)}(m)=1$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A006370","name":"The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd.","terms":"0,4,1,10,2,16,3,22,4,28,5,34,6,40,7,46,8,52,9,58,10,64,11,70,12,76,13,82,14,88,15,94,16,100,17,106,18,112,19,118,20,124,","url":"https://oeis.org/A006370"},{"id":"A008908","name":"a(n) = (1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached.","terms":"1,2,8,3,6,9,17,4,20,7,15,10,10,18,18,5,13,21,21,8,8,16,16,11,24,11,112,19,19,19,107,6,27,14,14,22,22,22,35,9,110,9,30,17","url":"https://oeis.org/A008908"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}