A090905 Left side of irregular triangle of natural numbers in which every row product is a multiple of the previous.

1, 2, 3, 5, 9, 15, 27, 47, 87, 167, 327, 635, 1263, 2519, 5007, 10007, 19947, 39875, 79739, 159399, 318779, 637503, 1274999, 2549979, 5099903, 10199787, 20399535, 40799063, 81598083, 163196135, 326392259, 652784499, 1305568943, 2611137839

Offset: 1

Author

Amarnath Murthy, Dec 13 2003

Keywords

• nonn

Comments

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.

Examples

			The triangle goes as follows:
(1)
(2),
(3,4),
(5,6,7,8),
(9,10,11,12,13,14),
(15,16,17,18,19,20,21,22,23,24,25,26)...
		

Crossrefs

Cf. A090904, A090906, A090907.

Programs

Mathematica

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 *)

Extensions

More terms from David Wasserman, Feb 10 2006