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%I A275013 #31 Apr 25 2020 08:43:15
%S A275013 2,7,26,97,241,2521,16022,26603,39343,104659,248407,506509,584213,
%T A275013 2560177,4036967,4417813,5167587,9725107,25045771,27489679,70416259,
%U A275013 111555371,174266683,359589563,1075714923,6820213333,15378035161,16598109467,19423306039,30133946677,74466436042
%N A275013 Lower ends of record gaps between numbers that are either primes or semiprimes.
%C A275013 This sequence is infinite, since the asymptotic density of the primes and semiprimes is 0. - _Charles R Greathouse IV_, Nov 12 2016
%H A275013 Giovanni Resta, <a href="/A275013/b275013.txt">Table of n, a(n) for n = 1..37</a> (terms < 10^13)
%F A275013 a(n) = A275014(n) - A275108(n).
%e A275013 a(5) = 241 because the next prime or semiprime after 241 is 247, and that is a record gap of size 6.
%o A275013 (PARI) r=0; last=2; for(n=3,1e9, if(bigomega(n)<3, if(n-last>r, r=n-last; print1(last", ")); last=n)) \\ _Charles R Greathouse IV_, Nov 12 2016
%o A275013 (PARI) checkrange(a,b,r)=while(b-a>r, forstep(n=a+r, a+1, -1, if(bigomega(n)<3, a=n; next(2))); for(n=a+r+1,b, if(bigomega(n)<3, return([a,n])))); 0
%o A275013 print1(2); p=5; r=1; forprime(q=7,1e9, if(q-p<=r, p=q; next); t=checkrange(p,q,r); while(t!=0, print1(", "t[1]); t=checkrange(t[2],q,r=t[2]-t[1])); p=q) \\ _Charles R Greathouse IV_, Nov 12 2016
%Y A275013 Cf. A037143, A111087, A275014, A275108.
%K A275013 nonn
%O A275013 1,1
%A A275013 _Bobby Jacobs_, Nov 12 2016
%E A275013 a(7)-a(31) from _Charles R Greathouse IV_, Nov 12 2016

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