Numbers n such that e^n is next to a prime number.

2, 3, 7, 149, 1097, 22027, 65659969, 5184705528587072464087, 3989519570547215850763757278730095398677254309, 14302079958348104463583671072905261080748384225250684971

1

This sequence grows radiply. Note that the plot shows this sequence with logarithms taken twice. There are four additional terms less than 10^10000.

T. D. Noe, Plot of 14 terms

T. D. Noe, Table of 14 terms

(Mma) t = Table[s = E^n; Floor[s], {n, 0, 3000}]; Union[Select[t, PrimeQ], Select[t + 1, PrimeQ]]

nonn

T. D. Noe, Aug 11 2014