[seqfan] Composite Hurwitz Zeta formulas for A007494 & A032766

Andras andras at yahoo.com
Fri Nov 10 02:58:07 CET 2017


I have two composite Hurwitz Zeta function formulas for "Numbers that are congruent to 0 or 2 mod 3." and "Numbers that are congruent to 0 or 1 mod 3." that I thought might be of some interest.

My question is if these 2 sequences merit their own entries (which would be A007494 & A032766 squared & omitting the Sqrt function in the formula) & if so what they should be named, or alternatively if they should instead be included in the formula sections for A007494 & A032766. Here are some domain colored visualizations of the functions: https://i.imgur.com/GGPG2E0.jpg , also, if anyone knows what these types of composite zeta functions are named, that'd be greatly appreciated! 
Mathematica Code:
ζ = HurwitzZeta

A007494 =  Function[{Z},   Sqrt[4 - 9/2 ζ[-1, 2/3 + Z] - 3 ζ[-1, 5/6] +     3 ζ[-1, 4/3] + 9/2 ζ[-1, 5/3] +     3 (-1)^Z ζ[-1, 5/6 + Z/2] -     3 (-1)^Z ζ[-1, 1/6 (2 + 3 Z)]]]
A032766 =  Function[{Z},   Sqrt[9 - 9/2 ζ[-1, 4/3 + Z] - 3 ζ[-1, 7/6] +     3 ζ[-1, 5/3] + 9/2 ζ[-1, 7/3] +     3 (-1)^Z ζ[-1, 7/6 + Z/2] -     3 (-1)^Z ζ[-1, 1/6 (4 + 3 Z)]]]
Table[N[A007494[n]], {n, 0, 25}]
Table[N[A032766[n]], {n, 0, 25}]



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