# [seqfan] Another problem sequence that needs your help.

Ed Jeffery ed.jeffery at yahoo.com
Thu Jun 30 04:55:49 CEST 2011

```Dear friends:

I recently submitted A192321={2, 6, 12, 630, 2312310, 4204200, 212219517510,...} to OEIS with only the seven terms shown here because they are so tough for me to generate with the limited resources I have. I thought afterward that the sequence was rather lame and expected it to be rejected, but, to my surprise, I was asked to extend it and give a program for generating the terms. The problem is that I am not a programmer, so I wonder if one of you out there might be interested in writing something in Pari, Mathematica or Maple and provide more terms.

A general term a(n) of the sequence has prime factorization

a(n)=2^d_(n,1)*3^d_(n,2)*5^d_(n,3)*...*p_(k_n)^d_(n,k_n),

where p_(k_n) is the (k_n)-th prime, and the sequence of exponents d_(n,1),...,d_(n,k_n) (of length k_n) is given by the sequence of k_n digits from the n-th term of J. H. Conway's Look and Say
sequence A005150(defined with initial value 1).

For example, from Conway we have A005150={1,11,21,1211,111221,312211,13112221,...}, so, for n=4, A005150(4)=1211 -> {1,2,1,1}, which implies k_4=4, with d_(4,1)=1, d_(4,2)=2, d_(4,3)=d_(4,4)=1; hence a(4) = 2*3^2*5*7 = 630.

I know of no relation between terms which is why I was/am skeptical. I also didn't make the above representation of a(n) clear enough in my submission, so I need to edit it.