A160500 - OEIS

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

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OFFSET

1,1

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

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A160440, A160370, A031928.

Sequence in context: A106281 A127341 A135316 * A327448 A046753 A033563

Adjacent sequences: A160497 A160498 A160499 * A160501 A160502 A160503