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

0,1

Links

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

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-pp<np-E^n, pp, np], {n, 0, 25}] (* James 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 *)

Crossrefs

Sequence in context: A122724 A256758 A033844 * A052919 A005807 A167422

Adjacent sequences: A037025 A037026 A037027 * A037029 A037030 A037031

Keyword

nonn

Author

G. L. Honaker, Jr.

Extensions

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

Status

approved