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%I #20 Oct 09 2023 11:19:40
%S 11,41,71,101,131,161,191,221,251,281,311,341,371,401,431,461,491,521,
%T 551,581,611,641,671,701,731,761,791,821,851,881,911,941,971,1001,
%U 1031,1061,1091,1121,1151,1181,1211,1241,1271,1301,1331,1361,1391,1421,1451
%N a(n) = 30*n + 11.
%C Possible lower bounds of twin primes pairs ending in 1.
%C 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 give 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.
%F From _R. J. Mathar_, Dec 05 2007: (Start)
%F O.g.f.: (11+19*x)/(-1+x)^2 = 19/(-1+x) + 30/(-1+x)^2.
%F a(n) = 30*n + 11. (End)
%e 41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
%t Range[11, 7000, 30] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%t 30*Range[0,50]+11 (* _Harvey P. Dale_, Oct 09 2023 *)
%o (PARI) forstep(x=11,1500,30,print1(x","))
%K easy,nonn
%O 0,1
%A _Cino Hilliard_, May 05 2007
%E Offset corrected by _Eric Rowland_, Aug 15 2017
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