"Pass Me By" is, indeed, the title of the song you're looking for. Released in 1964 off Frank's SOFTLY, AS I LEAVE YOU album, this rollicking tune was written by Cy Coleman and Carolyn Leigh and introduced in the movie "Father Goose," starring Cary Grant and Leslie Caron. The song also appears in Sinatra's THE COMPLETE REPRISE STUDIO RECORDINGS, released in 1995 and 1998. Both of these albums/collections are now out of print; however, you may be able to find a CD copy of SOFTLY, AS I LEAVE YOU on amazon.com. They're usually sold as "New," "Used," or "Collectible," but be prepared to shell out!! They don't come cheap. Happy hunting!! ".....when Sinatra paints a portrait, the tones and colors are his alone." ~Sid Mark~

Ted deCerchio
When I was "17" I visited Atlantic City, it was in the late 60's & I decided to see for myself the famous "500 Club" on Missouri Ave. It was in a rundown neighborhood by that time with "Club Harlem" right down the street, where Frank would visit Ella & Billie for a song or two.During the day the clubs were closed or probably no longer in operation.I walked around to the side entrance of the 500 club & saw that it was a small,intimate club, the kind Sinatra preferred.This was a getaway from the hustle of show business in New York, a stone's throw. The highlight was looking @ the hand & footprints on the front sidewalk of the club. I remember that Frank's hands were small for such an entertainment giant.
Around the year 2000 I revisited Atlantic City to see if the 500 Club was still extant. I went into a bar & asked if the Club was still around,& everyone in the bar laughed @ me, saying it had been torn down with the inception of the Casinos. I asked "What about the sidewalk handprints of Frank & Sammy?" they all said "gone", that "the only handprints you're going to see in A.C. are Michael Jackson's in front of Resorts." It's a shame not even a street sign or plaque remains where the 50's Rat Pack entertained themselves & others.
ted deCerchio