%I #10 Dec 15 2016 10:42:16
%S 1,2,3,5,9,15,27,47,87,167,327,635,1263,2519,5007,10007,19947,39875,
%T 79739,159399,318779,637503,1274999,2549979,5099903,10199787,20399535,
%U 40799063,81598083,163196135,326392259,652784499,1305568943,2611137839
%N Left side of irregular triangle of natural numbers in which every row product is a multiple of the previous.
%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.
%e The triangle goes as follows:
%e (1)
%e (2),
%e (3,4),
%e (5,6,7,8),
%e (9,10,11,12,13,14),
%e (15,16,17,18,19,20,21,22,23,24,25,26)...
%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, 17}]; a (* _Michael De Vlieger_, Dec 15 2016 *)
%Y Cf. A090904, A090906, A090907.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Dec 13 2003
%E More terms from _David Wasserman_, Feb 10 2006