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%I #12 Feb 08 2020 04:33:38
%S 19,97,197,461,659,1319,1451,2111,2309,2969,3167,3299,4157,5279,7127,
%T 9239,10889,11549,15971,16631,22637,25409,26729,29567,30491,34649,
%U 34847,55439,55901,64151,87119,92399,98009,110879,118799,152459,164999,176417
%N Primes p such that 11 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).
%C 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).
%H Amiram Eldar, <a href="/A080187/b080187.txt">Table of n, a(n) for n = 1..521</a> (terms below 10^11)
%e 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;
%e 461 is a term since 462 = 2*3*7*11 is the only number between 461 and the next prime 463.
%t maxPrime[n1_, n2_] := FactorInteger[#][[-1, 1]] & /@ Range[n1, n2]; Select[Range[180000], PrimeQ[#] && Max[maxPrime[# + 1, NextPrime[#] - 1]] == 11 &] (* _Amiram Eldar_, Feb 08 2020 *)
%o (PARI) {forprime(p=2,180000,q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=11,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a); j++); if(m==11,print1(p,",")))}
%Y Cf. A052248, A001359, A051038, A002473, A080195.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Feb 10 2003
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