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A117368 a(n) = largest prime less than the smallest prime dividing (2n-1).

%I A117368 #19 Apr 14 2019 20:37:08
%S A117368 2,3,5,2,7,11,2,13,17,2,19,3,2,23,29,2,3,31,2,37,41,2,43,5,2,47,3,2,
%T A117368 53,59,2,3,61,2,67,71,2,5,73,2,79,3,2,83,5,2,3,89,2,97,101,2,103,107,
%U A117368 2,109,3,2,5,7,2,3,113,2,127,5,2,131,137,2,7,3,2,139,149,2,3,151,2,5,157,2
%N A117368 a(n) = largest prime less than the smallest prime dividing (2n-1).
%C A117368 Placing a 1 between each term of this sequence gets sequence A117365.
%H A117368 Robert Israel, <a href="/A117368/b117368.txt">Table of n, a(n) for n = 2..10000</a>
%F A117368 From _Robert Israel_, Apr 14 2019: (Start)
%F A117368 a(n) = A151799(A090368(n)).
%F A117368 a(n) = 2*n-3 if 2*n-1 is in A006512. (End)
%e A117368 a(13) = 3 because smallest prime dividing 25 is 5 and largest prime less than 5 is 3.
%p A117368 with(numtheory): a:=proc(n): prevprime(factorset(2*n-1)[1]): end: seq(a(n),n=2..90); # _Emeric Deutsch_, Apr 22 2006
%t A117368 prs=Prime[Range[50]];
%t A117368 f[n_]:=NextPrime[First[Select[prs,Divisible[2 n-1,#]&]],-1]
%t A117368 f/@Range[2,90]  (* _Harvey P. Dale_, Jan 23 2011 *)
%Y A117368 Cf. A006512, A090368, A117365, A151799.
%K A117368 nonn
%O A117368 2,1
%A A117368 _Leroy Quet_, Mar 10 2006
%E A117368 More terms from _Emeric Deutsch_, Apr 22 2006