Kansas freshmen Jamari Traylor, left, and Ben McLemore watch the Late Night in the Phog festivities from the bench on Friday, Oct. 14, 2011 at Allen Fieldhouse.

Ben McLemore sat with his buddy — fellow ineligible Kansas University freshman Jamari Traylor — just a few rows behind the Jayhawk bench, cheering wildly during the latter stages of a 63-60 second-round NCAA Midwest Regional victory over Purdue on Sunday in Omaha’s CenturyLink Center.

Though KU trailed by as many as 11 points the first half, nine with 14 minutes left, three with 1:58 to play and one point with 59.9 seconds remaining, losing was the last thing on the Jayhawks’ minds.

“No one was thinking about that,” McLemore said. “We were thinking about moving forward, getting stops and scoring. I never thought we were going to lose.”

Thanks mainly to some late-game heroics by Elijah Johnson, Tyshawn Taylor and Thomas Robinson, the Jayhawks (29-6) did win and now advance to a Sweet 16 game against North Carolina State (24-12) at 9:17 p.m. Friday at the Edward Jones Dome in McLemore’s hometown of St. Louis.

“I mean, I am so proud of them,” McLemore said of his teammates, “and happy we get to go back to Lawrence and practice together again.

“It’s just a good feeling,” added McLemore, who along with the 6-8 Traylor has been able to practice all second semester but not play in games until next season in accordance with NCAA rules.

As one might expect, McLemore is fired up about making the short trip down I-70 to watch his teammates continue their postseason run.

“It’s great to go home, for us to go home, for me to go home,” the 6-foot-5, 185-pound McLemore said with a smile. “It’s spring break now. I’ll be happy to go home and see my family.

“It’s definitely a dream come true,” he added of the Jayhawks playing in St. Louis. “Hopefully we can do it next year, too, the same way. It’s not about going to St. Louis, it’s about us getting this win.”

The Jayhawks obviously won’t have much free time in St. Louis, but if given a chance, he plans to be a walking tour guide.

“I mean, everybody should know about the Arch,” he said of the Gateway Arch. “It’s mainly what we are known for. I might be able to take some of the players down to the Arch.

“You can go up there,” he added of taking a ride to the top. “They’ve got exhibits inside the Arch, too. Everybody loves going there when they visit St. Louis. It’s a good atmosphere there.”

McLemore was stumped when asked who he’d rank as the greatest athlete in St. Louis history.

“There have been so many,” he said.

He was able to quickly come up with his favorite pro player in St. Louis annals.

“I’ll give it to Larry Hughes (former NBA forward waived by Orlando on Feb. 1). I’ve met him before. I think he’s one of the greatest players to come out of St. Louis,” McLemore said.

McLemore — he averaged 28.3 points and 12.7 rebounds and 6.2 assists a game his junior year at St. Louis’ Wellston High before playing at Oak Hill Academy and Christian Life Center in Houston his senior year — is eager to play in his first game for the Jayhawks in 2012-13.

“Next year will be fun. I can’t wait,” he said. “Tyshawn (Taylor), (Conner) Teahan and maybe T-Rob (Thomas Robinson) will be gone, but Elijah (Johnson), Travis (Releford), Jamari … we’ll all be coming together. We have a great recruiting class coming in. I think it’ll be a great season.

“Jamari and I are playing well (at practice),” he added. We’ve tried to help the team get better every day. Mainly I’m guarding Tyshawn and Elijah and Conner and Travis Releford. Sometimes I guard the big men. I’m learning a lot, definitely.”

KU coach Bill Self has said the two have been great for the Red team — the scout team — at practice.

“I said today I wonder if it’s a coincidence we got better in the last eight weeks because those two are practicing,” Self said recently of McLemore and Traylor. “You can’t take possessions off (because of the active duo). They try hard and hold you accountable. They’ve helped our team.

“It’s unfortunate both had to deal with this,” he added of being ruled partial qualifiers. “We thought both had legitimate cases. The NCAA did make the ruling they did. Based on the ruling (sitting out first semester, practicing second), the two have done a good job making the most of it, turning a supposed negative into a positive, knowing they will have four (years) to play four left. Both have well above 3.0s (grade-point averages). If they stay four years, it almost certainly guarantees graduation. I think they spun it into a positive the best they can.

“The kids see themselves having some success, studying hard, with the right tutorial system, it’s great. I think this will be good for their lives the way it’s played out.”

Of their ability, Self said: “Talking raw athletes, Justin (Wesley) and Elijah (may be best on team) and Tyshawn is fastest. Ben and Jamari may be equals or better than those guys. They will give us an element of athleticism.”

T-Rob a finalist: KU junior Thomas Robinson is one of four finalists for Naismith College Basketball Player of the Year presented by AT&T, the Atlanta Tipoff Club announced Monday. Other finalists: Kentucky freshman Anthony Davis, Michigan State senior Draymond Green and Creighton sophomore Doug McDermott.

Next up: The No. 2-seeded Jayhawks on Friday will meet a red-hot No. 11-seed North Carolina State team that has won six of its last seven games, including Sunday’s 66-64 second-round win over No. 3-seed Georgetown.

N.C. State is 24-12 overall under first-year coach Mark Gottfried, nephew of former KU football coach Mike Gottfried. The squad went 15-16 a year ago under Sidney Lowe.

“They’ve been playing great the last couple of games. Man, they are on a roll now,” KU junior Jeff Withey said of the team that beat San Diego State, 79-65, in the first round. “It will be tough going against them. They beat Georgetown and are on a roll. We have a week to get prepared for them and to get ready.”

Never give up: Releford said the Jayhawks’ come-from-behind win over Purdue was especially satisfying.

“We competed and didn’t give up,” he said. “Getting close and them taking the lead again late, we had to continue to fight through it. It’s great. Another weekend of playing ball, another week of practicing and getting after it. That sounds great.”