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 A092332 For S a string of numbers, let F(S) = the product of those numbers. Let a(1)=1. For n>1, a(n) is the greatest k such that a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k] where each y_i is of positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k. 0

%I

%S 1,1,2,1,1,2,2,3,1,1,2,1,1,2,2,3,2,2,2,3,3,2,2,4,2,2,3,2,1,1,2,2,3,3,

%T 2,2,3,3,2,4,2,2,2,3,2,3,3,2,3,2,4,4,3,2,2,2,3,3,2,2,2,3,3,2,2,2,3,3,

%U 3,3,4,4,2,3,2,2,2,3,3,3,3,4,2,2,3,4,3,3,2,2,4,3,5,1,1,2,1,1,2,2,3,1,1,2,1

%N For S a string of numbers, let F(S) = the product of those numbers. Let a(1)=1. For n>1, a(n) is the greatest k such that a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k] where each y_i is of positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k.

%C Here [x][y] denotes concatenation of strings. This is Gijswijt's sequence, A090822, except that the 'y' blocks count as being equivalent whenever the product of their digits is the same.

%C For actually calculating this sequence, compare prime compositions of the products, not the products themselves, as those grow far too fast.

%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and _Allan Wilks_, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Sloane/sloane55.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.

%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and _Allan Wilks_, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].

%H <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>

%Y Cf. A090822, A091975, A091976.

%K nonn

%O 1,3

%A J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004

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