A160500 Prime p1 of consecutive primes p1, p2, where p2-p1=10, and p1, p2 are in different centuries.

691, 1399, 1699, 5791, 6091, 6691, 6793, 7297, 8599, 10993, 12391, 12799, 13999, 14197, 14293, 15091, 15391, 15991, 17599, 18493, 18691, 19699, 22699, 22993, 23899, 24499, 24799, 25693, 26893, 27397, 28099, 28297, 28393, 29191, 33493

Offset: 1

Author

Ki Punches, May 15 2009

Keywords

• nonn

Comments

The sequence is probably infinite.

It appears that every integer occurs as the difference round((a(n+1)-a(n))/100); all numbers 1..228 occur as these differences for a(n) < 1000000000. - Hartmut F. W. Hoft, May 18 2017

Examples

			Consecutive primes 10993 and 11003 differ by 10 and are in consecutive centuries, so 10993 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A160440, A160370, A031928.

Programs

Mathematica

a160500[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[100, n, 100]], First[#]-Last[#]==10&]]
a160500[33500] (* data *) (* Hartmut F. W. Hoft, May 18 2017 *)
cpdcQ[{a_,b_}]:=b-a==10&&Floor[a/100]!=Floor[b/100]; Select[Partition[Prime[Range[ 4000]],2,1],cpdcQ][[;;,1]] (* Harvey P. Dale, Sep 02 2024 *)

Extensions

Edited by Ray Chandler, May 22 2009