Q. about {0,1}-matrices.

[N. J. A. Sloane]

Dear seqfans,

Anyone with C++ may wish to add more terms?

Thanks, Zak

%S A000001
2,3,5,7,3,11,7,37,5,439,11,7013,379,27673,373,54973,977,548753,4229,7678313,10009,230339381,27763,5067438619,197297
%N A000001 a(1) =2 , a(2) = 3, a(n) = least prime such
that a(n-2) | (a(n)+a(n-1))
%A A000001 Zak Seidov  (zakseidov at gmail.com), Jan 07
2007


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This is related to a recent thread on seq.fan, but the topic is unique 
enough so as to deserve its own thread.

I have just posted the following two sequences to the OEIS:

>%S A127180 2,3,5,10,22,54,142,402
>%N A127180 a(n) = smallest possible (product of b(k)'s + product of 
>c(k)'s), where the positive integers <= n are partitioned somehow into 
>{b(k)} and {c(k)}.
>%C A127180 The maximum (product of b(k)'s + product of c(k)'s) occurs, for 
>n>=2, when {b(k)} = (2,3,4,...n) and {c(k)} = (1).
>
>a(1) = 2 because the product over the empty set is defined here as 1.
>%e A127180 By partitioning (1,2,3,...8) into {b(k)} and {c(k)} so that 
>{b(k)} = (1,4,6,8) and {c(k)} = (2,3,5,7), then (product of b(k)'s + 
>product of c(k)'s) is minimized. Therefore, a(8) = 1*4*6*8 + 2*3*5*7 = 402.
>%Y A127180 A127181
>%O A127180 1
>%K A127180 ,more,nonn,


>%S A127181 1,1,2,3,5,11,37,221,3361
>%N A127181 a(1)=a(2)=1. a(n) = smallest possible (product of b(k)'s + 
>product of c(k)'s), where the sequence's terms a(1) through a(n-1) are 
>partitioned somehow into {b(k)} and {c(k)}.
>%C A127181 Every term of the sequence is coprime to every other term.
>%e A127181 By partitioning (a(1),a(2),...a(7)) = (1,1,2,3,5,11,37) into 
>{b(k)} and {c(k)} so that {b(k)} = (1,2,5,11) and {c(k)} = (1,3,37), then 
>(product of b(k)'s + product of c(k)'s) is minimized. Therefore, a(8) = 
>1*2*5*11 + 1*3*37 = 221.
>%Y A127181 A127180
>%O A127181 1
>%K A127181 ,more,nonn,


First, like so many (almost every) of the sequences I submit, these 

Second, I have done something that submitters should never do, I 
being absolutely certain these terms are correct. Are they?

Third, I wonder what else can be said about these sequences, such as 
their asymptotics.

Thanks,
Leroy Quet