Fractional part of square root of a(n) starts with 3: first term of runs.

Terms

a(0) =11a(1) =19a(2) =29a(3) =40a(4) =54a(5) =69a(6) =87a(7) =107a(8) =128a(9) =152a(10) =177a(11) =205a(12) =235a(13) =266a(14) =300a(15) =335a(16) =373a(17) =413a(18) =454a(19) =498a(20) =543a(21) =591a(22) =641a(23) =692a(24) =746a(25) =801a(26) =859a(27) =919a(28) =980a(29) =1044