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A330427 Primes P where the nearest prime is greater than 3*log(P) away.

%I A330427 #30 Sep 08 2022 08:46:24
%S A330427 38501,58831,153191,203713,206699,232259,247141,250543,268343,279269,
%T A330427 286927,302053,330509,362521,362801,404597,413353,421559,430193,
%U A330427 438091,479081,479701,485263,504727,512207,515041,539573,539993,546781,569369,574859,590489,624917
%N A330427 Primes P where the nearest prime is greater than 3*log(P) away.
%C A330427 The author suggests that these numbers be called Triple Frogger Primes because three times the distance as the average distance to the nearest neighbor (the log) has to be hopped.
%H A330427 Robert Israel, <a href="/A330427/b330427.txt">Table of n, a(n) for n = 1..1000</a>
%p A330427 q:= 3: state:= false: count:= 0: Res:= NULL:
%p A330427 while count < 100 do
%p A330427   p:= nextprime(q);
%p A330427   newstate:= is(p-q > 3*log(q));
%p A330427   if state and newstate then
%p A330427     count:= count+1; Res:= Res, q;
%p A330427   fi;
%p A330427   q:= p; state:= newstate;
%p A330427 od:
%p A330427 Res; # _Robert Israel_, Dec 18 2019
%t A330427 Select[Prime@ Range[10^5], Min@ Abs[# - NextPrime[#, {-1, 1}]] > 3 Log[#] &] (* _Michael De Vlieger_, Dec 15 2019 *)
%o A330427 (Magma) f:=func<p|Abs(p-NextPrime(p)) gt 3*Log(p) and Abs(p-PreviousPrime(p)) gt 3*Log(p)>;  [p:p in PrimesUpTo(630000)|f(p)];// _Marius A. Burtea_, Dec 18 2019
%o A330427 (PARI) lista(nn) = {my(x=2, y=3); forprime(p=5, nn, if(min(p-y, y-x)>3*log(y), print1(y, ", ")); x=y; y=p); } \\ _Jinyuan Wang_, Mar 03 2020
%Y A330427 Cf. A288908 (with 1*log(P)), A330426 (with 2*log(P)), A330428 (Lowest Frogger Primes).
%K A330427 nonn
%O A330427 1,1
%A A330427 _Steven M. Altschuld_, Dec 14 2019
%E A330427 More terms from _Michael De Vlieger_, Dec 15 2019