question about {0,1}-matrices

[Jon Awbrey]

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one of my fav's, as it was my fav's fav, csp, 2 wit.
a metamessage b-ing the b-ing of higher order props:
(X -> B) -> B

ja

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I wrote, in part:
>...
>>%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)}.
>....

>>%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)}.
>>....

>First, like so many (almost every) of the sequences I submit, these 
>sequences need extending.
>Second, I have done something that submitters should never do, I 
>submitted the terms I calculated (by hand and with calculator) without 
>being absolutely certain these terms are correct. Are they?
>Third, I wonder what else can be said about these sequences, such as 
>their asymptotics.
>

I thanks Zak Seidov and Peter Pein for extending A127181.

I am glad to see that the few terms I have calculated are correct.

As for the asymptotics:
The nth term of A127180, for n >=2, is greater than, and probably
close to, 2*sqrt(n!), obviously.
I don't know if this can be improved upon, as far as asymptotics of 
A127180 are concerned.
As for A127181, the little bit that each term is greater than 
2*sqrt(product of earlier terms) perhaps will blow up later on. So I will 
not venture to say anything about this sequence's rate of ascension.

Thanks,
Leroy Quet