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%I #66 Nov 11 2016 09:43:28
%S 3,5,11,127,1151,1361,19661,31469,156007,360749,370373,1357333,
%T 2010881,17051887,20831533,191913031,436273291,2300942869,3842611109,
%U 4302407713,10726905041,25056082543,304599509051,461690510543,1346294311331,1408695494197,1968188557063,2614941711251,13829048560417,19581334193189
%N Primes q with prime gap q - p of n-th record merit.
%C The merit of the gap between consecutive primes p and q is (q-p)/log(p).
%C This sequence is infinite (Westzynthius 1931). - _Charles R Greathouse IV_, Nov 10 2016
%F a(n) = A111870(n) + A111871(n). - _Charles R Greathouse IV_, Nov 11 2016
%t p = 2; q = 3; lmt = 0; lst = {}; While[p < 10^12, If[q > p + lmt*Log[p], AppendTo[lst, q]; Print[q]; lmt = (q - p)/Log[p]]; p = q; q = NextPrime@ p]; lst (* or *)
%t (* set lst = the terms in A111870 *) NextPrime[ lst] (* _Robert G. Wilson v_, Nov 07 2016 *)
%o (PARI) r=rm=0; p=2; forprime(q=3,, t=q-p; if(t>r, r=t; t/=log(p); if(t>rm, rm=t; print1(q", "))); p=q) \\ _Charles R Greathouse IV_, Nov 11 2016
%Y Cf. A111870, A111871.
%K nonn
%O 1,1
%A _Bobby Jacobs_, Nov 07 2016
%E More terms from _Robert G. Wilson v_, Nov 07 2016
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