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

1,2

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.

Links

Table of n, a(n) for n=1..34.

Example

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)...

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 *)

Crossrefs

Cf. A090904, A090906, A090907.

Sequence in context: A293855 A022858 A301470 * A065956 A328078 A178738

Adjacent sequences: A090902 A090903 A090904 * A090906 A090907 A090908

Keyword

nonn

Author

Amarnath Murthy, Dec 13 2003

Extensions

More terms from David Wasserman, Feb 10 2006

Status

approved