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%I #35 Apr 25 2020 08:43:22
%S 3,9,29,101,247,2531,16033,26615,39359,104677,248426,506531,584237,
%T 2560202,4036993,4417843,5167619,9725141,25045807,27489719,70416301,
%U 111555415,174266734,359589619,1075714987,6820213399,15378035231,16598109538,19423306117,30133946758,74466436127
%N Upper ends of record gaps between numbers that are either primes or semiprimes.
%C This sequence is infinite, since the asymptotic density of the primes and semiprimes is 0. - _Charles R Greathouse IV_, Nov 12 2016
%H Giovanni Resta, <a href="/A275014/b275014.txt">Table of n, a(n) for n = 1..37</a> (terms < 10^13)
%F a(n) = A275013(n) + A275108(n).
%e a(5) = 247 because the next prime or semiprime after 241 is 247, and that is a record gap of size 6.
%o (PARI) r=0; last=2; for(n=3, 1e9, if(bigomega(n)<3, if(n-last>r, r=n-last; print1(n", ")); last=n)) \\ _Charles R Greathouse IV_, Nov 12 2016
%o (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 print1(3); 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[2]); t=checkrange(t[2], q, r=t[2]-t[1])); p=q) \\ _Charles R Greathouse IV_, Nov 12 2016
%Y Cf. A037143, A111087, A275013, A275108.
%K nonn
%O 1,1
%A _Bobby Jacobs_, Nov 12 2016
%E a(7)-a(31) from _Charles R Greathouse IV_, Nov 12 2016
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