A257891 Numbers that are products of at least three consecutive primes.

30, 105, 210, 385, 1001, 1155, 2310, 2431, 4199, 5005, 7429, 12673, 15015, 17017, 20677, 30030, 33263, 46189, 47027, 65231, 82861, 85085, 96577, 107113, 146969, 190747, 215441, 241133, 255255, 290177, 323323, 347261, 392863, 409457, 478661, 510510, 583573

Offset: 1

Author

Reinhard Zumkeller, May 12 2015

Keywords

• nonn

Examples

			a(5) = 1001 = 7 * 11 * 13;
a(6) = 1155 = 3 * 5 * 7 * 11;
a(7) = 2310 = 2 * 3 * 5 * 7 * 11;
a(8) = 2431 = 11 * 13 * 17.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A151800, A097889, A000977, A046301 (subsequence).

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a257891 n = a257891_list !! (n-1)
a257891_list = f $ singleton (30, 2, 5) where
   f s = y : f (insert (w, p, q') $ insert (w `div` p, a151800 p, q') s')
         where w = y * q'; q' = a151800 q
               ((y, p, q), s') = deleteFindMin s

Mathematica

Select[Module[{nn=1000},Flatten[Table[Times@@@Partition[Prime[Range[nn]],d,1],{d,3,7}]]]//Union,#<10^7&] (* Harvey P. Dale, Aug 04 2024 *)