A158277 The lesser of twin prime pairs with each prime in a different century.

599, 2999, 3299, 4799, 5099, 6299, 8999, 10499, 11699, 21599, 25799, 26699, 29399, 33599, 34499, 36899, 37199, 42899, 44699, 47699, 49199, 56099, 57899, 60899, 63599, 65099, 65699, 70199, 74099, 81899, 83399, 85199, 88799, 92399, 97499, 100799, 101999, 102299

Offset: 1

Author

Ki Punches, Mar 15 2009

Keywords

• nonn

Comments

The sequence is conjecturally infinite; note that those ending in 999 straddle millenia: A158861.

Since any prime greater than 3 is congruent to 1 or 5 modulo 6, a(n)+1 is divisible by 300 (see A001359). - Hartmut F. W. Hoft, May 18 2017

Links

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

Crossrefs

Cf. A060229, A158861, A001359, A060229.

Programs

Mathematica

Select[Range[100,110000,100],AllTrue[#+{1,-1},PrimeQ]&]-1 (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 21 2016 *)
a158277[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[100, n, 100]], First[#]-Last[#]==2&]]
a158277[105000] (* data *) (* Hartmut F. W. Hoft, May 18 2017 *)

Extensions

Corrected by Ray Chandler and R. J. Mathar, Apr 03 2009