This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128464 #22 Sep 08 2022 08:45:30
%S A128464 11,17,29,41,47,59,71,77,89,101,107,119,131,137,149,161,167,179,191,
%T A128464 197,209,221,227,239,251,257,269,281,287,299,311,317,329,341,347,359,
%U A128464 371,377,389,401,407,419,431,437,449,461,467,479,491,497,509,521,527,539
%N A128464 Numbers that are congruent to {11, 17, 29} mod 30.
%C A128464 Numbers of the form 30k+r, 0 < r < 30, that are possible lower bounds of twin prime pairs.
%C A128464 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 bound of a twin prime pair.
%H A128464 Vincenzo Librandi, <a href="/A128464/b128464.txt">Table of n, a(n) for n = 1..1000</a>
%H A128464 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A128464 From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F A128464 G.f.: x*(11+6*x+12*x^2+x^3)/((x-1)^2*(1+x+x^2)).
%F A128464 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A128464 a(n) = 10*n-1+4*sin(2*n*Pi/3)/sqrt(3).
%F A128464 a(3k) = 30k-1, a(3k-1) = 30k-13, a(3k-2) = 30k-19. (End)
%F A128464 E.g.f.: 1 + (10*x - 1)*exp(x) + 4*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2))/sqrt(3). - _Ilya Gutkovskiy_, Jun 15 2016
%e A128464 41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
%p A128464 A128464:=n->10*n-1+4*sin(2*n*Pi/3)/sqrt(3): seq(A128464(n), n=1..100); # _Wesley Ivan Hurt_, Jun 14 2016
%t A128464 Select[Range[0, 800], MemberQ[{11, 17, 29}, Mod[#, 30]] &] (* _Wesley Ivan Hurt_, Jun 14 2016 *)
%t A128464 LinearRecurrence[{1, 0, 1, -1}, {11, 17, 29, 41}, 100] (* _Vincenzo Librandi_, Jun 15 2016 *)
%o A128464 (PARI) g(n) = forstep(x=11,n,30,print1(x","x+6","x+18","))
%o A128464 (Magma) [n : n in [0..800] | n mod 30 in [11, 17, 29]]; // _Wesley Ivan Hurt_, Jun 14 2016
%K A128464 easy,nonn
%O A128464 1,1
%A A128464 _Cino Hilliard_, May 05 2007
%E A128464 Better name by _Omar E. Pol_, Oct 28 2013