A160370 Smaller member p of a pair (p,p+6) of consecutive primes in different centuries.

1097, 2897, 3797, 4597, 5297, 5897, 9397, 11497, 11897, 12197, 12497, 12697, 15797, 16097, 18797, 19597, 21997, 24097, 24197, 28597, 28697, 29297, 30097, 30197, 30697, 32497, 35597, 36997, 39097, 40897, 41597, 41897, 42397, 45497, 47297

Offset: 1

Author

Ki Punches, May 11 2009

Keywords

• nonn

Comments

Note that the smaller member of a pair of sexy primes with the same constraint on centuries defines a different sequence, since members of a sexy prime pair do not need to be *consecutive* primes.

The larger member in the pair is obtained by adding 6 to an entry.

Every a(n)+3 is a multiple of 100 such that neither a(n)+2 nor a(n)+4 are primes. It appears that every integer occurs as the difference round((a(n+1)-a(n))/100); all numbers 1..333 occur as these differences for a(n) < 1000000000. - Hartmut F. W. Hoft, May 18 2017

Examples

			30097 + 6 = 30103.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A158277, A046117, A023201.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[5000]],2,1],#[[2]]-#[[1]] == 6 && Floor[#[[1]]/100]!=Floor[#[[2]]/100]&]][[1]] (* Harvey P. Dale, Apr 28 2012 *)
a160370[n_] := Select[Range[97, n, 100], AllTrue[# + {0, 6}, PrimeQ] && NoneTrue[# + {2, 4}, PrimeQ]&]
a160370[49000] (* data *) (* Hartmut F. W. Hoft, May 18 2017 *)

Formula

{A031924(n): [A031924(n)/100] <> [A031925(n)/100]} where [..]=floor(..).

Extensions

Edited by R. J. Mathar, May 14 2009