A353085 a(n) = nextprime(A138198(n-1)). Largest of a pair of consecutive primes whose prime gap is the first occurrence of n^2 or -1 if such a gap never occurs.
3, 11, 1847, 9587, 89753, 396833, 11981587, 70396589, 1872852203, 10958688203, 47203303559, 767644375301, 8817792099037, 78610833115937, 497687231721941, 2069461000670881, 22790428875365903, 78944802602540033
Offset: 1