This is the exact example given in IRS Publication 969 on page 6 under "Enrolled in Medicare" (<a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/p969.pdf">https://www.irs.gov/pub/irs-pdf/p969.pdf</a>) - a man who is 65 went on Medicare in July, so while his normal HSA contribution limit would have been $4,400 ($3,400 plus $1,000), the 6 month pro-rated limit is 6/12ths his normal annual limit of $4,400. NOTE that Pub 969 has not been updated for 2018, but these examples are still valid, with the change of your annual limit to $3,450 (plus $1,000).
