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 A128468 a(n) = 30*n + 17. 8

%I

%S 17,47,77,107,137,167,197,227,257,287,317,347,377,407,437,467,497,527,

%T 557,587,617,647,677,707,737,767,797,827,857,887,917,947,977,1007,

%U 1037,1067,1097,1127,1157,1187,1217,1247,1277,1307,1337,1367,1397,1427,1457

%N a(n) = 30*n + 17.

%C Previous name was: Numbers of the form 30k+17 or possible lower members of twin primes pairs ending in 7.

%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 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 Numbers n such that n==7 (mod 10) and n==5 (mod 6). - _Vincenzo Librandi_, Jun 25 2014

%H Vincenzo Librandi, <a href="/A128468/b128468.txt">Table of n, a(n) for n = 0..1999</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Robert Israel_, Dec 10 2014: (Start)

%F G.f.: x*(13*x+17)/(x-1)^2.

%F E.g.f.: 13 + (30*x-13)*exp(x). (End)

%F a(n) = 2*a(n-1) - a(n-2) for n >= 2. - _Jinyuan Wang_, Mar 10 2020

%e 17 = 30*0 + 17, the lower part of the twin prime pair 17,19.

%p seq(30*n+17, n=0..100); # _Robert Israel_, Dec 10 2014

%t Range[17, 7000, 30] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%o (PARI) g(n) = forstep(x=17,n,30,print1(x","))

%Y Cf. A001359.

%K nonn,easy

%O 0,1

%A _Cino Hilliard_, May 05 2007

%E Offset changed to 0, new name from _Joerg Arndt_, Dec 11 2014

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Last modified April 23 06:03 EDT 2021. Contains 343199 sequences. (Running on oeis4.)