Fractional part of square root of a(n) starts with 6: first term of runs.

Terms

a(0) =7a(1) =13a(2) =22a(3) =32a(4) =44a(5) =58a(6) =74a(7) =93a(8) =113a(9) =135a(10) =159a(11) =185a(12) =214a(13) =244a(14) =276a(15) =310a(16) =346a(17) =385a(18) =425a(19) =467a(20) =511a(21) =557a(22) =606a(23) =656a(24) =708a(25) =762a(26) =818a(27) =877a(28) =937a(29) =999