He has had an almost reverse experience to Scott as his Open debut got off to a tricky start. Olesen began with five bogeys in hist first 10 holes before claiming a much-needed birdie on 16th.
On Friday, he was a model of consistency and made an impressive 18 pars in his second round.
He is now just one shot back from Scott on five-over and is living the dream.
Olesen said: “It is what I have dreamt of ever since I was a kid, getting to be in these positions. I think I held my own pretty well.
“I was quite nervous on the front nine and that is why my score was bad, but I played the last 26 holes bogey-free, and I am pretty proud of that and will take a lot from it.”
Luis Masaveu was out in the morning and started with seven consecutive pars. As the wind picked up, he started to drop shots and four bogeys in six holes threatened to derail his bid.
However, he finished with five straight pars to keep his chances alive and then watched as the cut was pushed to six-over. He starts on Saturday just two strokes back from Scott.
That’s the same score as Tommy Morrison. He was in, then he was out and finally he was back in again, birdieing the 16th and holing an 11-foot par putt on 17 to make the weekend.
The 152nd Open started with 12 amateurs in the field, the most since 1987, but eight have seen their Championship come to an end.
Matthew Dodd-Berry, who made it through Final Qualifying, had started positively with a one-over 72 after the first round, before an 80 on Friday ended his hopes.
Jasper Stubbs also ended on 10-over for the Championship but showed great resilience in making two birdies to begin his second round having gone out of bounds with his first tee shot on Thursday.
There were no such problems for Jaime Montojo who began his major debut with an eagle on the first hole.