I figuring out the whistling at the beginning of "The Gold Bug," and in doing so, I realized that it's the same melody that's played on brass at the beginning of "May Be a Price to Pay." I'd never noticed that before.
In "May be a Price to Pay," that melody is in D minor, and in "The Gold Bug," it's in A minor with a few extra trills. So it's not exactly the same, but essentially it's the same melody.