A051102 Floor of exp(n-th prime).

7, 20, 148, 1096, 59874, 442413, 24154952, 178482300, 9744803446, 3931334297144, 29048849665247, 11719142372802611, 639843493530054949, 4727839468229346561, 258131288619006739623, 104137594330290877971834, 42012104037905142549565934, 310429793570191990870734214

Offset: 1

Author

Joel Patrick Hollins (s1161557(AT)cedarville.edu)

Keywords

• nonn

Examples

			e = 2.718281828..., e^5 = 148.4131591..., floor( e^5 ) = 148.
		

References

• Kumanduri and Romero, "Number Theory", Upper Saddle River, NJ, 1998.

Links

• T. D. Noe, Table of n, a(n) for n=1..100

Crossrefs

Cf. A000040, A000149, A001113.

Programs

Mathematica

Floor[Exp[#]]&/@Prime[Range[20]] (* Harvey P. Dale, Dec 12 2012 *)

Python

from sympy import floor, E, prime
def a(n):  return floor(E**prime(n))
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jul 20 2021

Formula

a(n) = A000149(A000040(n)). - Alois P. Heinz, Apr 09 2020