duplicates

[Ralf Stephan]

> %S A107755 2,8,12,26,30,36,38,80,84,90,92
> %N A107755 Numbers n such that Sum_{k=1..n} Catalan(k) == 0 mod 3.
> 
> %S A107756 1,4,5,6,7,10,13,14,15,16,17,18,19,20,21,22,23,24,25,28,31,
> %N A107756 Numbers n such that Sum_{k=1..n} Catalan(k) == 1 mod 3.
> %F A107756 Equivalently, numbers n such that base 3 expansion of n+1 contains a 2.
> 
> %S A107757 3,9,11,27,29,35,39,81,83,89,93
> %N A107757 Numbers n such that Sum_{k=1..n} Catalan(k) == 2 mod 3.
> 
> I don't know if this is anything more than a coincidence.   NJAS


What else? There is a 1:100 chance to hit a k-regular sequence in the OEIS.
That's not too small.  Comments:

%Y A107755 Equals 2*A074938.
%Y A107756 Equals A074940 - 1.
%Y A107757 Equals A074939 - 1.


ralf