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Join[{35}, Select[Partition[Select[Range[3000], NumberDigit[Sqrt[#], -1] == 9&], 2, 1], (#[[2]]-#[[1]]!=1&)][[All, 2]]] (* _or *) LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {35, 48, 63, 80, 99, 119, 142}, 50] (* _Harvey P. Dale_, Aug 14 2021 *)
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Join[{35}, Select[Partition[Select[Range[3000], NumberDigit[Sqrt[#], -1] == 9&], 2, 1], (#[[2]]-#[[1]]!=1&)][[All, 2]]] (* Harvey P. Dale, Aug 14 2021 *)
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Decimal Fractional part of square root of a(n) starts with 9: first term of runs.
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