It’s been 58 years since Neil Sedaka had his first Top 40 hit on the Billboard Hot 100 singles chart, and 56 years since he performed in Hawaii for the first time in August 1959, but the classically trained pianist is still adding career firsts to his resume. Sedaka’s concert at the Blaisdell Concert Hall on Saturday will be the first time he’s shared a stage with Yvonne Elliman, and he’s looking forward to it.

He’ll have some “firsts” to share with the audience, too.

“I just finished a couple of songs a few days ago. I’ve never played them in public, so I’m going to debut them in Hawaii and see what the reaction is,” Sedaka said during a March 22 phone call from a Los Angeles hotel.

He continues to write six decades after he and his original writing partner, Howard Greenfield, hit the pop charts with a string of hits — “The Diary,” “Stairway to Heaven,” “Calendar Girl,” “Breaking Up Is Hard to Do” and “Next Door to an Angel,” to name five. The fact is, Sedaka never stopped writing. Even when his career in the United States was eclipsed by the British Invasion of the mid-1960s, he was writing and performing in other parts of the world.

Then, in 1974, the Captain & Tennille recorded “Love Will Keep Us Together,” a song Sedaka had written and previously recorded, and Tennille ad-libbed the phrase “Sedaka is back” on the fade-out. And Sedaka was back as a hit-making American recording artist and songwriter.

“That was very nice of them to do,” Sedaka said of the duo. “She’s a great singer. I had three or four songs recorded by them.”

Sedaka had another string of his own chart hits of between 1974 and 1978 — including a dramatically different arrangement of “Breaking Up Is Hard to Do.” Several years later he recorded “Should Have Never Let You Go” with his daughter, Dara; the duet peaked at No. 19 on the Hot 100 single chart.

For everyone who’s keeping track, Sedaka was eligible for induction into the Rock and Roll Hall of Fame when the first group of honorees was inducted in 1986, and he has been eligible for induction every year since.

“My songs always had a message,” Sedaka said. “They were mostly romantic songs, but I always try to do a story where the lyrics were very understandable and people could relate. ‘Breaking Up Is Hard to Do’ — when I came up with that title, little did I know how universal that was.

“I get emails from all over the world from people who say that they’re down, physically or emotionally, and they put on the records and it gives them a lift.”

Sedaka started taking piano lessons in the second grade and earned a scholarship to Juilliard at the age of 8. In 1952 he was introduced to a neighbor, Howard Greenfield, who was an aspiring lyricist. By the time he was 18, he and Greenfield were a professional song-writing team and working in the Brill Building in New York, a center of the American pop music industry.

Their colleagues/competitors at the Brill Building included the songwriting teams of Barry Mann and Cynthia Weil, Jeff Berry and Ellie Greenwich, and Gerry Goffin and Carole King.

Sedaka’s first hit as a recording artist, “Oh! Carol,” was inspired by King — they’d dated in high school. Goffin, the lyricist of the Goffin-King songwriting team (and King’s husband at the time), wrote an “answer song” titled “Oh! Neil” that King recorded and released as a single later that year. It was not a hit, and King’s career as a recording artist did not take off until her Brill Building days were long gone.

King is not the only person who has inspired a Sedaka hit. In 1975 Sedaka wrote and recorded “The Immigrant,” which was inspired by the American government’s efforts to deport John Lennon. “He was very moved,” Sedaka recalled.

Eventually they met, and Lennon said, “Usually people call me to get favors, but you called me to say that you’re dedicating a song to me.”

Sedaka says he was influenced by classic songwriting duos such as the Gershwins and Rodgers and Hart — and volunteered that meeting Richard Rodgers, one of the greatest composers in Broadway history, made him “nervous as a catfish.”

“I was a very good friend of his daughter, Mary Rodgers. She was very impressed with my music, and she set up a meeting with me and Richard Rodgers in his office on Madison Avenue around 1975. I was nervous as a catfish,” Sedaka recalled. “I had my best suit and tie on, I walked in, he had already heard one of my albums that Mary gave to him, and he was very impressed. I sat at the piano and played some new songs at the time, and he said, ‘Come away from the piano, that’s too easy for you. Come back with an idea for a Broadway show. I’d like to write one with you.’

“I was very into my career of concerts at the time, so I was stupid, I never pursued it,” he said. “I guess I was scared. But I had the thrill of meeting him.”

Sedaka’s archives are full of photos of artists he did work with. Elton John, a self-described Sedaka fan, helped relaunch Sedaka’s career in the United States in the early 1970s by signing him to his Rocket Record Co. label and then harmonized with him on “Bad Blood.” The song topped the Hot 100 for three weeks in 1975. Bette Midler joined him on his NBC television special “Steppin’ Out” in 1976.

Toni Tennille was a special guest when he celebrated his 50th anniversary in show business at Lincoln Center in 2007. Other guest performers included David Foster, Connie Francis and Natalie Cole.

“Sixty years of writing — I think it’s 63 years of writing now,” he said. “Over 700 songs. It’s big body of work.”