A090904 - OEIS

%I #12 Dec 22 2016 23:30:44

%S 1,2,12,1680,2162160,4626053752320000,

%T 13644281345408020027550269440000,

%U 4402827357584746886229433170489943024971625310770489684257669120000000000

%N Row products of the irregular triangle defined in A090905.

%C Conjecture: For n > 4 the last term of the n-th group is 2p where p is the largest prime in the (n-1)th group. And these are the Bertrand primes.

%H Michael De Vlieger, <a href="/A090904/b090904.txt">Table of n, a(n) for n = 1..11</a> (Term 12 has 1865 decimal digits.)

%e a(3) = 1680 because a(1) is the product of 1 successive number starting with 1 = 1, a(2) is the product of 1 successive number (2) = 2, a(3) is the product of 2 successive numbers (3,4) = 12, finally a(4) is the product of 4 successive numbers (5,6,7,8) = 1680. All the products have the property that a(n) = 0 (mod a(n - 1)). Thus a(4) = 1680. - _Michael De Vlieger_, Dec 22 2016

%t a = {{1, 1}}; Do[k = Last@ a[[i - 1]]; While[! Divisible[Pochhammer[Total@ a[[i - 1]], k], Pochhammer @@ a[[i - 1]]], k++]; AppendTo[a, {Total@ a[[i - 1]], k}], {i, 2, 8}]; Pochhammer @@ # & /@ a (* _Michael De Vlieger_, Dec 15 2016 *)

%Y Cf. A090905, A090906, A090907.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Dec 13 2003

%E More terms from _David Wasserman_, Feb 10 2006