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A128473 Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair.

%I A128473 #31 Jan 06 2025 21:06:08
%S A128473 23,53,83,113,143,173,203,233,263,293,323,353,383,413,443,473,503,533,
%T A128473 563,593,623,653,683,713,743,773,803,833,863,893,923,953,983,1013,
%U A128473 1043,1073,1103,1133,1163,1193,1223,1253,1283,1313,1343,1373,1403,1433,1463
%N A128473 Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair.
%C A128473 30*k + 23 -+ 2 is a multiple of 3 or 5 precluding it from being part of a twin prime pair.
%H A128473 Vincenzo Librandi, <a href="/A128473/b128473.txt">Table of n, a(n) for n = 1..1000</a>
%H A128473 Albert van der Horst, <a href="http://home.hccnet.nl/a.w.m.van.der.horst/hcc96.txt">Counting Twin Primes</a>
%H A128473 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A128473 From _Vincenzo Librandi_, Feb 15 2018: (Start)
%F A128473 G.f.: x*(23 + 7*x)/(1 - x)^2.
%F A128473 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%t A128473 Range[23, 7000, 30] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%t A128473 CoefficientList[Series[(23 + 7 x) / (1 - x)^2, {x, 0, 50}], x] (* _Vincenzo Librandi_, Feb 15 2018 *)
%t A128473 LinearRecurrence[{3,-3,1},{23,53,83},50] (* or *) NestList[#+30&,23,50] (* _Harvey P. Dale_, Sep 11 2019 *)
%o A128473 (PARI) g(n) = forstep(x=23,n,30,print1(x","))
%o A128473 (Magma) [30*n+23: n in [0..50]]; // _Vincenzo Librandi_, Feb 15 2018
%o A128473 (Magma) I:=[23,53,83]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 15 2018
%Y A128473 Subsequence of A110673.
%K A128473 nonn,easy
%O A128473 1,1
%A A128473 _Cino Hilliard_, May 06 2007