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 A386523 #9 Aug 14 2025 12:03:59 %S A386523 1,4,1,4,2,1,5,6,8,6,2,7,4,5,0,9,8,0,3,9,2,1,5,6,8,6,2,7,4,5,0,9,8,0, %T A386523 3,9,2,1,5,6,8,6,2,7,4,5,0,9,8,0,3,9,2,1,5,6,8,6,2,7,4,5,0,9,8,0,3,9, %U A386523 2,1,5,6,8,6,2,7,4,5,0,9,8,0,3,9,2,1,5,6,8,6,2,7,4,5,0,9,8,0,3,9 %N A386523 Decimal expansion of 577/408. %C A386523 Baudhayana used the fraction 577/408 to approximate sqrt(2) (see Tattersall). %C A386523 Periodic of period 16. %C A386523 8th convergent of sqrt(2). %D A386523 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 257. %H A386523 Wikipedia, <a href="https://en.wikipedia.org/wiki/Baudhayana">Baudhayana</a>. %H A386523 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1). %F A386523 a(n) = a(n-16) for n > 20. %F A386523 G.f.: (1 + 4*x + x^2 + 4*x^3 + 2*x^4 + x^5 + 5*x^6 + 6x^7 + 8*x^8 + 6*x^9 + 2*x^10 + 7*x^11 + 4*x^12 + 5*x^13 + 9*x^15 + 7*x^16 - 4*x^17 + 2*x^18 + 5*x^19)/(1 - x^16). %F A386523 Equals A001333(8)/A000129(8). %e A386523 1.414215686274509803921568627450980392156862745... %t A386523 RealDigits[577/408,10,100][[1]] %Y A386523 Cf. A000129, A001333, A002193, A375743. %K A386523 nonn,cons,easy %O A386523 1,2 %A A386523 _Stefano Spezia_, Jul 24 2025