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

1,1

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

Links

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

Formula

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

Example

30097 + 6 = 30103.

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 *)

Crossrefs

Cf. A158277, A046117, A023201.

Sequence in context: A203807 A184470 A234722 * A123366 A186476 A096926

Adjacent sequences: A160367 A160368 A160369 * A160371 A160372 A160373

Keyword

nonn

Author

Ki Punches, May 11 2009

Extensions

Edited by R. J. Mathar, May 14 2009

Status

approved