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A080186 Primes p such that 7 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248). 2

%I

%S 13,41,419,881,1049,2267,2687,3359,3527,5879,6299,7349,7559,8231,8819,

%T 10499,18521,26249,26879,28349,29399,30869,33599,35279,49391,81647,

%U 100799,102059,131249,131711,134399,158759,170099,183707,197567,241919

%N Primes p such that 7 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 13 and the lesser of twin primes q (A001359) such that q+1 is 7-smooth (A002473) but not 5-smooth (A051037, A080194).

%H Harvey P. Dale, <a href="/A080186/b080186.txt">Table of n, a(n) for n = 1..100</a>

%e 13 is a term since 14 = 2*7, 15 = 3*5, 16 = 2^4 are the numbers between 13 and the next prime 17; 419 is a term since 420 = 2^2*3*5*7 is the only number between 419 and the next prime 421.

%t lpf7Q[n_]:=Max[Flatten[Transpose[FactorInteger[#]][[1]]&/@Range[ n+1, NextPrime[ n]-1]]]==7; Select[Prime[Range[22000]],lpf7Q] (* _Harvey P. Dale_, Sep 25 2015 *)

%o (PARI) {forprime(p=2,250000,q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=7,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a); j++); if(m==7,print1(p,",")))}

%Y Cf. A052248, A001359, A002473, A051037, A080194.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 10 2003

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)