A117879 First semiprime after e^n.

4, 4, 9, 21, 55, 155, 407, 1099, 2981, 8105, 22033, 59881, 162757, 442417, 1202611, 3269021, 8886117, 24154953, 65659981, 178482301, 485165203, 1318815739, 3584912849, 9744803447, 26489122131, 72004899341, 195729609431

Offset

0,1

Comments

Semiprime analog of A074496 = first prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = e. There are numbers where floor(e^n) is itself a semiprime, as with floor(e^6) = 403 = 13 * 31, floor(e^15) = 3269017 = 773 * 4229, floor(e^20) = 485165195 = 5 * 97033039, floor(e^22) = 3584912846 = 2 * 1792456423, floor(e^24) = 26489122129 = 103 * 257175943.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, e-Prime.

Formula

a(n) = Smallest semiprime > e^n. Smallest semiprime > floor(e^n). a(n) = min{s > A000149(n) and s in A001358}.

Mathematica

fsa[n_]:=Module[{i=1, c=Floor[E^n]}, While[PrimeOmega[c+i]!=2, i++]; c+i]; Array[fsa, 30, 0] (* Harvey P. Dale, Oct 18 2013 *)

Crossrefs

Cf. A000040, A000149, A001358, A007512, A014210, A050808, A050809, A059303, A064118, A095935, A115019, A074496, A118840.

Sequence in context: A067553 A112683 A192030 * A334009 A069549 A118069

Adjacent sequences: A117876 A117877 A117878 * A117880 A117881 A117882

Keyword

easy,nonn,less

Author

Jonathan Vos Post, May 02 2006

Status

approved