A083697a(n) = 2^(2^n - 1) * Fibonacci(2^n).

1, 2, 24, 2688, 32342016, 4677882957791232, 97861912906883207538212742365184, 42829440312913272520181533609472356498655100482256687829780267008

The first 2 terms appear at position 148.

…84460955058223172535940812848111745028410270193852…
position 148
termsstringfirst positionoccurrences
11199,997,334
21214810,000,708
3122466099,981
41224268862,040,7585

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.