A130789 The primes prime(n) sorted according to increasing prime(n)/prime(n+1).

3, 7, 2, 5, 13, 23, 19, 31, 11, 47, 113, 17, 53, 37, 61, 43, 89, 73, 83, 139, 29, 199, 67, 211, 181, 79, 41, 293, 131, 317, 241, 97, 151, 103, 157, 109, 167, 283, 173, 523, 59, 127, 337, 71, 233, 467, 1327, 163, 409, 251, 421, 509, 257, 263, 887, 359, 271, 193

Offset: 1

Author

R. J. Mathar, Jul 15 2007

Keywords

• nonn

Comments

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.

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

Examples

			3/5 < 7/11 < 2/3 < 5/7 < 13/17 < 23/29 < 19/23 < 31/37 < 11/13 < ...
Numerators of this chain of inequalities define the sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Gaps
• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

Crossrefs

Cf. A107664, A111870.

Programs

Mathematica

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