A090906 Row lengths of the irregular triangle defined in A090905.

1, 1, 2, 4, 6, 12, 20, 40, 80, 160, 308, 628, 1256, 2488, 5000, 9940, 19928, 39864, 79660, 159380, 318724, 637496, 1274980, 2549924, 5099884, 10199748, 20399528, 40799020, 81598052, 163196124, 326392240, 652784444, 1305568896, 2611137796

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.

Crossrefs

Cf. A090904, A090905, 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}]; Last /@ a (* Michael De Vlieger, Dec 15 2016 *)

Formula

For n>4 a(n)= 2*(A006992(n)-A006992(n-1)) - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004

Extensions

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004

More terms from David Wasserman, Feb 10 2006