[seqfan] Re: A135044

[Charles Greathouse]

I wrote a quick independent program and also found a(8) = 23.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Jan 27, 2014 at 12:44 PM, Hans Havermann <gladhobo at teksavvy.com>wrote:

> It's embarrassing to admit but I (generally) can't untangle definitions
> that involve a lot of letters, complicated here by underscores (and the
> comments leave me none the wiser). I even struggled with the given example
> and finally decided to just reverse engineer some possible logic by
> stepping through the initial terms. I'm assuming that the primes are {2, 3,
> 5, 7, 11, ...} and the composites {4, 6, 8, 9, 10, ...}, offsets 1.
>
> a(2) is composite (opposite of prime, since 2 is prime) #1, the 1 coming
> from a(1).
> a(3) is composite (opposite of prime, since 3 is prime) #4, the 4 coming
> from a(2).
> a(4) is prime (opposite of composite, since 4 is composite) #1, the 1
> coming from a(1).
> a(5) is composite (opposite of prime, since 5 is prime) #9, the 9 coming
> from a(3).
> a(6) is prime (opposite of composite, since 6 is composite) #4, the 4
> coming from a(2).
> a(7) is composite (opposite of prime, since 7 is prime) #2, the 2 coming
> from a(4).
> a(8) is prime (opposite of composite, since 8 is composite) #9, the 9
> coming from a(3). Except it's not. I predicted 23 here and instead it's 13
> (prime #6).
>
> On Jan 27, 2014, at 9:40 AM, Antti Karttunen <antti.karttunen at gmail.com>
> wrote:
>
> > http://oeis.org/A135044
> > "a(1)=1, then a(p_n)=c_a(n), a(c_n)=p_a(n), where p_n - n-th prime, c_n
> - n-th composite."
>
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