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A128468 a(n) = 30*n + 17.

%I A128468 #42 Mar 10 2020 10:28:44
%S A128468 17,47,77,107,137,167,197,227,257,287,317,347,377,407,437,467,497,527,
%T A128468 557,587,617,647,677,707,737,767,797,827,857,887,917,947,977,1007,
%U A128468 1037,1067,1097,1127,1157,1187,1217,1247,1277,1307,1337,1367,1397,1427,1457
%N A128468 a(n) = 30*n + 17.
%C A128468 Previous name was: Numbers of the form 30k+17 or possible lower members of twin primes pairs ending in 7.
%C A128468 For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a lower twin prime pair. The 30k+r wheel gives the recurrence 1, 7,11,13,17,19,23,29 31,37,41,43,47,49,53,59 .. which is frequently used in prime number sieves to skip multiples of 2,3,5. The fact that adding 2 to 30k+1,7,13,19,23 will gives us a multiple of 3 or 5, precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11,17,29 as the only possible cases to form a lower member of a twin prime pair.
%C A128468 Numbers n such that n==7 (mod 10) and n==5 (mod 6). - _Vincenzo Librandi_, Jun 25 2014
%H A128468 Vincenzo Librandi, <a href="/A128468/b128468.txt">Table of n, a(n) for n = 0..1999</a>
%H A128468 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A128468 From _Robert Israel_, Dec 10 2014: (Start)
%F A128468 G.f.: x*(13*x+17)/(x-1)^2.
%F A128468 E.g.f.: 13 + (30*x-13)*exp(x). (End)
%F A128468 a(n) = 2*a(n-1) - a(n-2) for n >= 2. - _Jinyuan Wang_, Mar 10 2020
%e A128468 17 = 30*0 + 17, the lower part of the twin prime pair 17,19.
%p A128468 seq(30*n+17, n=0..100); # _Robert Israel_, Dec 10 2014
%t A128468 Range[17, 7000, 30] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%o A128468 (PARI) g(n) = forstep(x=17,n,30,print1(x","))
%Y A128468 Cf. A001359.
%K A128468 nonn,easy
%O A128468 0,1
%A A128468 _Cino Hilliard_, May 05 2007
%E A128468 Offset changed to 0, new name from _Joerg Arndt_, Dec 11 2014