A037028 Prime closest to e^n.

2, 3, 7, 19, 53, 149, 401, 1097, 2971, 8101, 22027, 59879, 162751, 442399, 1202603, 3269011, 8886109, 24154957, 65659969, 178482289, 485165237, 1318815713, 3584912833, 9744803443, 26489122147, 72004899319

Offset: 0

Author

G. L. Honaker, Jr.

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..500

Programs

Mathematica

NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; Do[ a = Round[ N[ E^n ] ]; b = NextPrime[ Round[ N[ E^n ] ] - 1 ]; c = PrevPrime[ Round[ N[ E^n ] ] + 1 ]; If[ b - N[ E^n ] > N[ E^n ] - c, Print[ c ], Print[ b ] ], {n, 0, 25} ]
Table[np=NextPrime[E^n];pp=NextPrime[E^n,-1];If[E^n-ppJames C. McMahon, Dec 25 2024 *)
pce[n_]:=Module[{c=E^n,np,pp},np=NextPrime[c];pp=NextPrime[c,-1];Nearest[{pp,np},c]]; Array[pce,30,0]//Flatten (* Harvey P. Dale, Jan 30 2025 *)

Extensions

Corrected and extended by Robert G. Wilson v, Sep 16 2000