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%I #8 Dec 24 2023 01:07:25
%S 7,29,59,149,179,239,269,599,809,1619,2999,4049,4799,8999,9719,15359,
%T 21599,23039,33749,138239,179999,281249,345599,737279,3455999,6143999,
%U 6560999,10124999,13668749,15551999,17495999,20995199,22118399,23999999
%N Primes p such that 5 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).
%C The sequence consists of 7 and the lesser of twin primes q (A001359) such that q+1 is 5-smooth (A051037) but not 3-smooth (A003586, A080193).
%H Amiram Eldar, <a href="/A080185/b080185.txt">Table of n, a(n) for n = 1..1000</a>
%e 7 is a term since 8 = 2^3, 9 = 3^3, 10 = 2*5 are the numbers between 7 and the next prime 11; 149 is a term since 150 = 2*3*5^2 is the only number between 149 and the next prime 151.
%o (PARI) {forprime(p=2,24000000,q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=5,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a); j++); if(m==5,print1(p,",")))}
%Y Cf. A052248, A001359, A051037, A003586, A080193.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Feb 10 2003
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