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 A130789 #15 Feb 16 2025 08:33:06
%S A130789 3,7,2,5,13,23,19,31,11,47,113,17,53,37,61,43,89,73,83,139,29,199,67,
%T A130789 211,181,79,41,293,131,317,241,97,151,103,157,109,167,283,173,523,59,
%U A130789 127,337,71,233,467,1327,163,409,251,421,509,257,263,887,359,271,193
%N A130789 The primes prime(n) sorted according to increasing prime(n)/prime(n+1).
%C A130789 Or: primes sorted according to decreasing ratio A001223(n)/A000040(n). All values are conjectural, derived from the finite list up to prime(200000): large prime gaps at higher indices may still insert numbers above prime(200000) at low positions of the sequence.
%C A130789 Using a table of prime gaps, it is easy to determine that the sequence is correct for all primes < 10^18. - _T. D. Noe_, Jul 17 2007
%H A130789 T. D. Noe, <a href="/A130789/b130789.txt">Table of n, a(n) for n = 1..10000</a>
%H A130789 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>
%H A130789 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]
%e A130789 3/5 < 7/11 < 2/3 < 5/7 < 13/17 < 23/29 < 19/23 < 31/37 < 11/13 < ...
%e A130789 Numerators of this chain of inequalities define the sequence.
%t A130789 With[{nn=60},Take[Transpose[SortBy[Partition[Prime[Range[20*nn]],2,1], #[[1]]/ #[[2]]&]][[1]],nn]] (* _Harvey P. Dale_, Dec 03 2014 *)
%Y A130789 Cf. A107664, A111870.
%K A130789 nonn
%O A130789 1,1
%A A130789 _R. J. Mathar_, Jul 15 2007