A080187 Primes p such that 11 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).

19, 97, 197, 461, 659, 1319, 1451, 2111, 2309, 2969, 3167, 3299, 4157, 5279, 7127, 9239, 10889, 11549, 15971, 16631, 22637, 25409, 26729, 29567, 30491, 34649, 34847, 55439, 55901, 64151, 87119, 92399, 98009, 110879, 118799, 152459, 164999, 176417

Offset: 1

Author

Klaus Brockhaus, Feb 10 2003

Keywords

• nonn

Comments

The sequence appears to consist of 19, 97 and the lesser of twin primes q (A001359) such that q+1 is 11-smooth (A051038) but not 7-smooth (A002473, A080195).

Examples

			97 is a term since 98 = 2*7^2, 99 = 3^2*11, 100 = 2^2*5^2 are the numbers between 97 and the next prime 101;
461 is a term since 462 = 2*3*7*11 is the only number between 461 and the next prime 463.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..521 (terms below 10^11)

Crossrefs

Cf. A052248, A001359, A051038, A002473, A080195.

Programs

Mathematica

maxPrime[n1_, n2_] := FactorInteger[#][[-1, 1]] & /@ Range[n1, n2]; Select[Range[180000], PrimeQ[#] && Max[maxPrime[# + 1, NextPrime[#] - 1]] == 11 &] (* Amiram Eldar, Feb 08 2020 *)

PARI

{forprime(p=2,180000,q=nextprime(p+1); m=0; j=p+1; while(j