This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099879 #16 Aug 19 2025 10:31:26 %S A099879 1,9,4,2,6,5,5,4,2,2,7,6,3,9,8,7,3,2,8,2,2,1,4,1,3,2,9,1,4,1,2,6,6,7, %T A099879 2,3,7,6,8,8,0,7,3,6,3,0,0,0,7,1,1,5,5,1,5,1,0,0,5,6,9,5,6,1,7,7,7,6, %U A099879 3,2,2,3,0,8,8,9,3,4,3,4,6,5,9,7,1,5,3,2,0,8,0,6,7,5,0,1,6,8,5,3,9,8,0 %N A099879 Decimal expansion of a nested radical: sqrt(1^2 + sqrt(2^2 + sqrt(3^2 + ... %H A099879 Herman P. Robinson, <a href="/A257574/a257574.pdf">The CSR Function</a>, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy. %e A099879 1.94265542276398732822141329141266723768807363... %t A099879 k = 64; r = 65; While[k > 0, r = Sqrt[k^2 + r]; k-- ]; RealDigits[r, 10, 111][[1]] (* _Robert G. Wilson v_, Nov 04 2004 *) %o A099879 (PARI) t=0; forstep(n=100,1,-1,t=sqrt(t+n^2)); print(t) %o A099879 (PARI) \\ We need about b/log(b) steps, where epsilon = 2^-b. %o A099879 my(b=bitprecision(1.),t); forstep(n=b\log(b)+9,1,-1, t=sqrt(t+n^2)); t \\ _Charles R Greathouse IV_, Aug 19 2025 %Y A099879 Cf. A072449, A099874, A099876 to A099878 for other nested radicals. %K A099879 cons,easy,nonn %O A099879 1,2 %A A099879 Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 03 2004