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

1,1

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

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

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

Cf. A000040, A080192, A052248.

Sequence in context: A229106 A118849 A049561 * A073350 A167773 A049545

Adjacent sequences: A080188 A080189 A080190 * A080192 A080193 A080194

Keyword

nonn

Author

Klaus Brockhaus, Feb 10 2003

Status

approved