Interesting Seq ? Partition in groups with semiprime sums

zak seidov zakseidov at
Sat Jul 2 05:38:31 CEST 2005

Dear seqfan gurus,
i dare submit this sequence with hope
that someone may wish to answer
the Qs in it,
thanks, zak

%I A109411
%S A109411 
%N A109411 Partition of sequence of natural numbers in
the minimal 
groups such that sum of terms in each group is a
%C A109411 The partiton starts as this: 
The sequence A109411 gives the number of terms in each
The big question is: is the sequence finite? If a
group begins with a 
and ends with b then sum of terms is s=(a+b)(a-b+1)/2
and it's not 
evident that :
a) there are a's such that it's impossible to find
b>=a such that s 
is semiprime,  
b) such a's will appear in A109411. I leave it to
seqfans. I present 
"dirty" Mmca (as is) which works. The longest group
found is {1770-1843} 
consisting of 74 terms.
%t A109411 
%O A109411 1
%K A109411 ,nice,nonn,unkn,
%A A109411 Zak Seidov (zakseidov at, Jul 01

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