[seqfan] A135044

[Hans Havermann]

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."