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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.
4
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 269, 271, 277, 281, 283, 293, 307, 313
OFFSET
1,1
COMMENTS
Complement of A080192 relative to A000040.
From Flávio V. Fernandes, May 26 2021: (Start)
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].
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.
For all n, the largest prime < 2*a(n) is a term of A059788. (End)
LINKS
FORMULA
f(precprime(2*p)) = p, where f is the mapping defined by A052248.
EXAMPLE
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.
MATHEMATICA
Select[Range[300], PrimeQ[#] && NextPrime[2*#] < 2 * NextPrime[#] &] (* Amiram Eldar, Feb 07 2020 *)
PROG
(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, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Feb 10 2003
STATUS
approved