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EXAMPLE
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For k = 3, 4, ..., 33, {Prime[k], Mod[Prime[k], 6]} = {5, 5}, {7, 1}, {11, 5}, {13, 1}, {17, 5}, {19, 1}, {23, 5}, {29, 5}, {31, 1}, {37, 1}, {41, 5}, {43, 1}, {47, 5}, {53, 5}, {59, 5}, {61, 1}, {67, 1}, {71, 5}, {73, 1}, {79, 1}, {83, 5}, {89, 5}, {97, 1}, {101, 5}, {103, 1}, {107, 5}, {109, 1}, {113, 5}, {127, 1}, {131, 5}, {137, 5}, so a(n) = 5, 5, 5, 5, 5, 5, 5, 89, 89 for n = 1, 2, ..., 9 with a(10) > 89.
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