a(n) = the largest integer whose square has n digits and first digit 1.

Terms

a(0) =1a(1) =4a(2) =14a(3) =44a(4) =141a(5) =447a(6) =1414a(7) =4472a(8) =14142a(9) =44721a(10) =141421a(11) =447213a(12) =1414213a(13) =4472135a(14) =14142135a(15) =44721359a(16) =141421356a(17) =447213595a(18) =1414213562a(19) =4472135954a(20) =14142135623a(21) =44721359549a(22) =141421356237a(23) =447213595499