The C-motivic Steenrod algebra cohomology contains an indecomposable family e0 g_{2^n-1} in degrees (2^n-1)(20,4,12)+(17,4,10), with h1-localization to v_n and sparse w1-periodicity.
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A sparse periodic family in the cohomology of the $\mathbb{C}$-motivic Steenrod algebra
The C-motivic Steenrod algebra cohomology contains an indecomposable family e0 g_{2^n-1} in degrees (2^n-1)(20,4,12)+(17,4,10), with h1-localization to v_n and sparse w1-periodicity.