A080191 - OEIS

%I #28 Jul 16 2021 06:34:37

%S 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 109,113,127,131,137,139,151,157,163,167,173,179,181,191,193,197,199,

%U 211,223,227,229,233,239,241,251,257,269,271,277,281,283,293,307,313

%N 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 Complement of A080192 relative to A000040.

%C From _Flávio V. Fernandes_, May 26 2021: (Start)

%C 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 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 For all n, the largest prime < 2*a(n) is a term of A059788. (End)

%H Amiram Eldar, <a href="/A080191/b080191.txt">Table of n, a(n) for n = 1..10000</a>

%F f(precprime(2*p)) = p, where f is the mapping defined by A052248.

%e 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 Select[Range[300], PrimeQ[#] && NextPrime[2*#] < 2 * NextPrime[#] &] (* _Amiram Eldar_, Feb 07 2020 *)

%o (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 Cf. A000040, A080192, A052248.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 10 2003