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A276827 Primes p such that the greatest prime factor of 3*p+1 is at most 5.

%I A276827 #14 Sep 20 2016 03:06:47
%S A276827 3,5,13,53,83,853,2083,3413,5333,85333,208333,218453,341333,3495253,
%T A276827 5461333,8533333,13981013,83333333,853333333,22369621333,218453333333,
%U A276827 341333333333,2236962133333,3665038759253,53333333333333,91625968981333,203450520833333,1333333333333333
%N A276827 Primes p such that the greatest prime factor of 3*p+1 is at most 5.
%C A276827 Prime(i) such that A087273(i) <= 5.
%H A276827 Robert Israel, <a href="/A276827/b276827.txt">Table of n, a(n) for n = 1..1645</a>
%p A276827 N = 10^20: # to get all terms <= N
%p A276827 Res:= {}:
%p A276827 for a from 0 to ilog2(floor((3*N+1)/5)) do
%p A276827   twoa:= 2^a;
%p A276827   for b from (a mod 2) by 2 do
%p A276827     p:= (twoa*5^b-1)/3;
%p A276827     if p > N then break fi;
%p A276827     if isprime(p) then
%p A276827       Res:= Res union {p};
%p A276827     fi
%p A276827 od od:
%p A276827 sort(convert(Res,list));
%t A276827 Select[Prime@ Range[10^6], FactorInteger[3 # + 1][[-1, 1]] <= 5 &] (* _Michael De Vlieger_, Sep 19 2016 *)
%o A276827 (PARI) list(lim)=my(v=List(),s,t); lim=lim\1*3 + 1; for(i=0,logint(lim\2,5), t=if(i%2,2,4)*5^i; while(t<=lim, if(isprime(p=t\3), listput(v,p)); t<<=2)); Set(v) \\ _Charles R Greathouse IV_, Sep 19 2016
%Y A276827 Cf. A087273.
%Y A276827 Contains A093671, A093674, and A093676.
%K A276827 nonn
%O A276827 1,1
%A A276827 _Robert Israel_, Sep 19 2016