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A207820 Let A = A025584. a(n) is the smallest A(m) such that the interval (A(m)*n, A(m+1)*n) contains no primes from A.

%I A207820 #21 Feb 13 2013 23:58:29
%S A207820 2,2,2,1783,967,1663,3187,4813,13873,20347,1783,2617,27743,14533,
%T A207820 54829,71143,66169,46687,44119,57787,79609,552883,21397,297079,
%U A207820 1187107,89017,798697,285763,761377,2660587,812047,1463257,2795059,2816239,2676727,3069607,2500297
%N A207820 Let A = A025584. a(n) is the smallest A(m) such that the interval (A(m)*n, A(m+1)*n) contains no primes from A.
%C A207820 Conjecture. For n>=3, every a(n) is the lesser of a pair of cousin primes p and p+4, cf. A023200.
%C A207820 The limit of a(n) as n goes to infinity is infinity.
%t A207820 Table[aPrime[[NestWhile[#1+1&,1,!(nextAPrime[n aPrime[[#1]]]>n aPrime[[#1+1]])&]]],{n,2,20}]
%o A207820 (PARI) is_a025584(x) = isprime(x) && !isprime(x-2)
%o A207820 a025584_next(n) = {local(p); p=n+1; while(!is_a025584(p), p=p+1); p}
%o A207820 no_a025584(a,b) = {local(x,r); r=1; for(x=a+1, b-1, if(is_a025584(x), r=0)); r}
%o A207820 a207820(n) = {local(r,rp); rp=2; r=3; while(!no_a025584(n*rp, n*r), rp=r; r=a025584_next(r)); rp} \\ _Michael B. Porter_, Jan 20 2013
%Y A207820 Cf. A025584, A023200, A195325.
%K A207820 nonn
%O A207820 1,1
%A A207820 _Vladimir Shevelev_ and _Peter J. C. Moses_, Jan 10 2013
%E A207820 a(21)-a(37) from _Michael B. Porter_, Jan 20 2013