%I #6 Aug 04 2024 15:43:06

%S 30,105,210,385,1001,1155,2310,2431,4199,5005,7429,12673,15015,17017,

%T 20677,30030,33263,46189,47027,65231,82861,85085,96577,107113,146969,

%U 190747,215441,241133,255255,290177,323323,347261,392863,409457,478661,510510,583573

%N Numbers that are products of at least three consecutive primes.

%H Reinhard Zumkeller, <a href="/A257891/b257891.txt">Table of n, a(n) for n = 1..1000</a>

%e a(5) = 1001 = 7 * 11 * 13;

%e a(6) = 1155 = 3 * 5 * 7 * 11;

%e a(7) = 2310 = 2 * 3 * 5 * 7 * 11;

%e a(8) = 2431 = 11 * 13 * 17.

%t 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 *)

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a257891 n = a257891_list !! (n-1)

%o a257891_list = f $ singleton (30, 2, 5) where

%o f s = y : f (insert (w, p, q') $ insert (w `div` p, a151800 p, q') s')

%o where w = y * q'; q' = a151800 q

%o ((y, p, q), s') = deleteFindMin s

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 12 2015