A130789 - OEIS

%I #14 Mar 05 2023 13:27:04

%S 3,7,2,5,13,23,19,31,11,47,113,17,53,37,61,43,89,73,83,139,29,199,67,

%T 211,181,79,41,293,131,317,241,97,151,103,157,109,167,283,173,523,59,

%U 127,337,71,233,467,1327,163,409,251,421,509,257,263,887,359,271,193

%N The primes prime(n) sorted according to increasing prime(n)/prime(n+1).

%C 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 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 T. D. Noe, <a href="/A130789/b130789.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]

%e 3/5 < 7/11 < 2/3 < 5/7 < 13/17 < 23/29 < 19/23 < 31/37 < 11/13 < ...

%e Numerators of this chain of inequalities define the sequence.

%t With[{nn=60},Take[Transpose[SortBy[Partition[Prime[Range[20*nn]],2,1], #[[1]]/ #[[2]]&]][[1]],nn]] (* _Harvey P. Dale_, Dec 03 2014 *)

%Y Cf. A107664, A111870.

%K nonn

%O 1,1

%A _R. J. Mathar_, Jul 15 2007