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.

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

Author

Klaus Brockhaus, Feb 10 2003

Keywords

• nonn

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)

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A080192, A052248.

Programs

Mathematica

Select[Range[300], PrimeQ[#] && NextPrime[2*#] < 2 * NextPrime[#] &] (* Amiram Eldar, Feb 07 2020 *)

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
				

Formula

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