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%I #8 Sep 17 2012 11:21:39
%S 3,23,61,331,2837,18169
%N Fortunate numbers with increasing multiplicity.
%C a(n) appears in A005235 more often than any preceding term.
%C Is this sequence infinite?
%e 3 is the first term of A005235, so a(1) = 3. A005235(5) = A005235(8) = 23, while smaller primes appear only once, so a(2) = 23.
%o (PARI) ct(p)=my(pr=1,s);forprime(q=2,p-1,if(!ispseudoprime((pr*=q)+p), next);forprime(r=q+1,p-1,if(ispseudoprime(pr+r),next(2)));s++);s
%o r=0;forprime(p=2,2e3,t=ct(p);if(t>r,r=t;print1(p", ")))
%Y Cf. A005235, A046066.
%K nonn,hard,more
%O 1,1
%A _Charles R Greathouse IV_, Sep 06 2012
%E a(6) from _Charles R Greathouse IV_, Sep 17 2012