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A080191 Primes p such that p is the largest of all prime factors of the numbers between the prime preceding 2*p and the next prime.

%I A080191 #28 Jul 16 2021 06:34:37
%S A080191 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,61,67,73,79,83,89,97,103,
%T A080191 109,113,127,131,137,139,151,157,163,167,173,179,181,191,193,197,199,
%U A080191 211,223,227,229,233,239,241,251,257,269,271,277,281,283,293,307,313
%N A080191 Primes p such that p is the largest of all prime factors of the numbers between the prime preceding 2*p and the next prime.
%C A080191 Complement of A080192 relative to A000040.
%C A080191 From _Flávio V. Fernandes_, May 26 2021: (Start)
%C A080191 Equivalently, primes p such that p is the largest of all prime factors of the numbers in the interval [2*p, nextprime(2*p)-1].
%C A080191 For any prime p, if p is not the largest of all prime factors of the numbers in that interval (i.e., if p is not a term of this sequence), then the largest of all prime factors of the numbers in that interval will be a prime q that occurs in the number 2*q.
%C A080191 For all n, the largest prime < 2*a(n) is a term of A059788. (End)
%H A080191 Amiram Eldar, <a href="/A080191/b080191.txt">Table of n, a(n) for n = 1..10000</a>
%F A080191 f(precprime(2*p)) = p, where f is the mapping defined by A052248.
%e A080191 5 is a term since 7 is the prime preceding 2*5, 11 is the next prime and 5 is the largest of all prime factors of 8, 9 and 10.
%t A080191 Select[Range[300], PrimeQ[#] && NextPrime[2*#] < 2 * NextPrime[#] &] (* _Amiram Eldar_, Feb 07 2020 *)
%o A080191 (PARI) {forprime(k=2,317,p=precprime(2*k); q=nextprime(p+1); m=0; for(j=p+1,q-1,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a)); if(m==k,print1(k,",")))}
%Y A080191 Cf. A000040, A080192, A052248.
%K A080191 nonn
%O A080191 1,1
%A A080191 _Klaus Brockhaus_, Feb 10 2003