1,2

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.

Michael De Vlieger, Table of n, a(n) for n = 1..11 (Term 12 has 1865 decimal digits.)

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

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 *)

Cf. A090905, A090906, A090907.

Sequence in context: A235857 A085912 A085895 * A125295 A222065 A389339

Adjacent sequences: A090901 A090902 A090903 * A090905 A090906 A090907

Amarnath Murthy, Dec 13 2003

More terms from David Wasserman, Feb 10 2006

approved