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A216944 The least odd prime p for which the n-th prime can be written as 3p + q - 3 for some odd prime q.

%I A216944 #17 Mar 08 2018 21:14:18
%S A216944 3,3,3,3,3,3,5,3,5,3,3,3,3,7,3,5,3,3,5,3,7,5,3,3,3,3,7,7,3,5,5,5,3,3,
%T A216944 7,3,3,7,5,5,3,3,5,5,11,3,3,3,5,5,3,3,3,11,3,5,3,5,11,7,3,3,7,3,11,5,
%U A216944 3,3,7,3,3,11,3,7,5,5,7,5,5,5,3,5,3,7,5,3,3
%N A216944 The least odd prime p for which the n-th prime can be written as 3p + q - 3 for some odd prime q.
%C A216944 Conjecture: Any prime >= 11 can be written this way.
%H A216944 Robert Israel, <a href="/A216944/b216944.txt">Table of n, a(n) for n = 5..10000</a>
%e A216944 The corresponding q and prime(n): (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (19,31), (31,37), (29,41), (37,43), (41,47), (47,53), (53,59), (43,61), (61,67), (67,73), (73,79), (71,83), (83,89), (79,97), (89,101), (97,103), (101,107), (103,109), (107,113), (109,127), (113,131), (131,137), (127,139), (137,149), (139,151), (151,157), (157,163), (149,167), (167,173), (173,179), (163,181), (179,191), (181,193), (191,197), (193,199), (199,211), (211,223), (197,227), (223,229), (227,233), (233,239), (229,241), (239,251), (251,257), (257,263), (263,269), (241,271),  (271,277), (269,281), (277,283), (281,293), (277,307), (293,311), (307,313), (311,317), (313,331), (331,337), (317,347), (337,349), (347,353), (353,359), (349,367), (367,373), (373,379), (353,383), (383,389), (379,397), (389,401), (397,409), (401,419), (409,421), (419,431), (421,433), (433,439), (431,443), (443,449), (439,457), (449,461), (457,463), (461,467), (467,479).
%p A216944 f:= proc(n) local p,q;
%p A216944   p:= 2;
%p A216944   while 3*p<n+3 do
%p A216944     p:= nextprime(p);
%p A216944     if isprime(n-3*p+3) then return p fi;
%p A216944   od;
%p A216944 FAIL
%p A216944 end proc:
%p A216944 p:= 7: Res:= NULL:
%p A216944 for i from 1 to 100 do
%p A216944 p:= nextprime(p); Res:= Res, f(p);
%p A216944 od:
%p A216944 Res; # _Robert Israel_, Mar 08 2018
%o A216944 (PARI) a(n)=my(r=prime(n)+3); forprime(p=3,r\3-1,if(isprime(r-3*p), return(p))) \\ _Charles R Greathouse IV_, Dec 07 2014
%K A216944 nonn
%O A216944 5,1
%A A216944 _Marius Coman_, Sep 20 2012
%E A216944 New name from _Charles R Greathouse IV_, Dec 07 2014
%E A216944 Corrected by _Charles R Greathouse IV_, Dec 07 2014