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 A249973 #20 Jan 12 2015 03:05:41 %S A249973 1,1,1,2,1,2,1,2,1,1,2,3,1,2,1,3,2,1,3,2,1,3,2,1,1,2,3,4,1,2,3,1,4,2, %T A249973 1,3,2,4,1,3,2,1,4,3,2,1,4,3,2,1,1,2,3,4,5,1,2,3,4,1,2,5,3,1,4,2,1,3, %U A249973 5,2,4,1,3,2,5,1,4,3 %N A249973 Positive integers A when the positive roots of r^2 = Ar + B are listed in increasing order. %C A249973 Generalize the Fibonacci sequence recurrence equation as: F_(n+1) = A*F_n + B*F_(n-1), where A and B are positive integers. As n goes to infinity, the ratio F_n / F_(n-1) approaches the positive real number r = (A + sqrt(A*A + 4B))/2. This sequence gives the A values in increasing order of r. %C A249973 In case of a tie in r values, then sort in increasing order of sqrt(A*A + B*B). %C A249973 This A sequence appears to be the ordinal transform of the B sequence (A249974) and vice versa. The associative arrays of A and B are transposes. The first row of A's associative array seems to be A006000. %C A249973 For the A and B values leading to a positive integer limit r see a comment in A063929. - _Wolfdieter Lang_, Jan 12 2015 %e A249973 a(6) = 2 because the 6th smallest value of r (approximately 2.732050808) is that for A=2, B=2. %o A249973 (PARI) \\ see A249974 %Y A249973 Cf. A249974, A006000. %K A249973 easy,nonn %O A249973 1,4 %A A249973 _Kerry Mitchell_, Nov 09 2014 %E A249973 Edited. - _Wolfdieter Lang_, Jan 11 2015