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 A275976 #8 Mar 19 2017 19:38:14 %S A275976 5,1,5,5,1,2,4,3,4,0,0,7,4,6,4,4,0,5,5,1,4,1,6,1,9,3,3,7,5,6,5,2,2,8, %T A275976 2,8,7,4,8,5,7,6,0,4,5,1,8,8,1,1,0,0,2,4,8,3,1,4,3,1,1,0,7,7,6,9,7,3, %U A275976 5,0,2,9,8,8,6,6,9,4,6,6,3 %N A275976 Decimal expansion of a constant relating to the density of Fibonacci integers. %C A275976 Let F(x) be the number of Fibonacci integers, A178772, less than or equal to x. Then exp(c*sqrt(log x) - (log x)^e) < F(x) < exp(c*sqrt(log x) + (log x)^(1/6 + e)) for any e > 0, where c is this constant. Luca, Pomerance, & Wagner conjecture that 1/6 can be replaced by 0, and note that it can be replaced by 1/8 on a strong form of the abc conjecture. %H A275976 Florian Luca, Carl Pomerance, Stephan Wagner, <a href="http://dx.doi.org/10.1016/j.jnt.2010.09.010">Fibonacci Integers</a>, J. Number Theory 131 (2011), pp. 440-457. <a href="http://www.math.dartmouth.edu/~carlp/fibinttalk.pdf">[conference version]</a> %F A275976 2*zeta(2)*sqrt(zeta(3)/zeta(6)/log(phi)) where phi = (1 + sqrt(5))/2 is the golden ratio. %e A275976 5.1551243400746440551416193375652282874857604518811002483143110776973502988669... %t A275976 RealDigits[2 Zeta[2] Sqrt[Zeta[3]/Zeta[6]/Log[GoldenRatio]], 10, 81][[1]] (* _Indranil Ghosh_, Mar 19 2017 *) %o A275976 (PARI) phi=(sqrt(5)+1)/2 %o A275976 2*zeta(2)*sqrt(zeta(3)/zeta(6)/log(phi)) %Y A275976 Cf. A178772. %K A275976 nonn,cons %O A275976 1,1 %A A275976 _Charles R Greathouse IV_, Aug 31 2016