Conjectures 111-113 from "100 Conjectures from the OEIS". Correction.

[Antti Karttunen]

David Wilson wrote:

>>>  a(n) = 3 or -3 iff n in 3*A036556 [...]
>>>
>>> then would mean that A065359(n) = 3 or -3 <==> n is an odious number 
>>> which is multiple of 3.
>>
>
> No, A065356((2^(12k+6)-1)/3) = 6k+3.
>
 
Yes, your A065356((2^(12k+6)-1)/3) = 6k+3 gives with k=1 the same 
counterexample
87381 which I gave.

So the equivalence was disproved,
but that the implication holds, that I already proved.

Note that Ralf actually uses the implication arrow ==> (instead of <==>) 
in his
100 conjectures paper (conjectures 111 & 112):
(Found at http://me.in-berlin.de/~rws/mathpub.html )

> The truth is
>
> a(n) = odd multiple of 3 iff n in 3*A036556.
>
With this I agree.


Cheers,

Antti