# [seqfan] Re: Chain of semiprimes: a(n)=least semiprime p*q such that a(n-1)=p+q.

Hans Havermann pxp at rogers.com
Fri Sep 10 22:32:16 CEST 2010

```zak seidov:

> Chain of semiprimes:
> a(n) = the least semiprime p*q such that a(n-1)=p+q
> (p<=q both prime).
>
> For a(1)=6 we have:
> 6,9,14,33,62,*177*.

Going backwards yields a slightly less restrictive take on the
definition:
a(n) = least semiprime (p*q), iterating a(n+1) = p+q, that generates a
chain of n semiprimes:

1 {4}

2 {9, 6}
3 {14, 9, 6}
4 {33, 14, 9, 6}
5 {62, 33, 14, 9, 6}
6 {177, 62, 33, 14, 9, 6}

7 {886, 445, 94, 49, 14, 9, 6}
8 {2649, 886, 445, 94, 49, 14, 9, 6}
9 {5294, 2649, 886, 445, 94, 49, 14, 9, 6}
10 {68653, 5294, 2649, 886, 445, 94, 49, 14, 9, 6}

11 {496966, 248485, 49702, 24853, 886, 445, 94, 49, 14, 9, 6}
12 {1490889, 496966, 248485, 49702, 24853, 886, 445, 94, 49, 14, 9, 6}

13 {16896262, 8448133, 496966, 248485, 49702, 24853, 886, 445, 94, 49,
14, 9, 6}
14 {185858761, 16896262, 8448133, 496966, 248485, 49702, 24853, 886,
445, 94, 49, 14, 9, 6}

```