A080188 Primes p such that 13 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).

23, 311, 349, 857, 1091, 1871, 1949, 2027, 2339, 2729, 3119, 3821, 5849, 6551, 7487, 9437, 10139, 10529, 11699, 15287, 18251, 21059, 21839, 38609, 42899, 49919, 51479, 57329, 61151, 65519, 69497, 70199, 70979, 81899, 97499, 108107, 109199, 114659

Offset: 1

Author

Klaus Brockhaus, Feb 10 2003

Keywords

• nonn

Comments

The sequence appears to consist of 23, 349 and the lesser of twin primes q (A001359) such that q+1 is 13-smooth (A080197) but not 11-smooth (A051038, A080196).

Examples

			349 is a term since 350 = 2*5^2*7, 351 = 3^3*13, 352 = 2^5*11 are the numbers between 349 and the next prime 353; 857 is a term since 858 = 2*3*11*13 is the only number between 857 and the next prime 859.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1092 (terms below 10^11)

Crossrefs

Cf. A052248, A001359, A080197, A051038, A080196.

Programs

Mathematica

maxPrime[n1_, n2_] := FactorInteger[#][[-1, 1]] & /@ Range[n1, n2]; Select[Range[120000], PrimeQ[#] && Max[maxPrime[# + 1, NextPrime[#] - 1]] == 13 &] (* Amiram Eldar, Feb 08 2020 *)

PARI

{forprime(p=2,120000,q=nextprime(p+1); m=0; j=p+1; while(j