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%I #30 Sep 08 2022 08:46:24
%S 38501,58831,153191,203713,206699,232259,247141,250543,268343,279269,
%T 286927,302053,330509,362521,362801,404597,413353,421559,430193,
%U 438091,479081,479701,485263,504727,512207,515041,539573,539993,546781,569369,574859,590489,624917
%N Primes P where the nearest prime is greater than 3*log(P) away.
%C 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 Robert Israel, <a href="/A330427/b330427.txt">Table of n, a(n) for n = 1..1000</a>
%p q:= 3: state:= false: count:= 0: Res:= NULL:
%p while count < 100 do
%p p:= nextprime(q);
%p newstate:= is(p-q > 3*log(q));
%p if state and newstate then
%p count:= count+1; Res:= Res, q;
%p fi;
%p q:= p; state:= newstate;
%p od:
%p Res; # _Robert Israel_, Dec 18 2019
%t Select[Prime@ Range[10^5], Min@ Abs[# - NextPrime[#, {-1, 1}]] > 3 Log[#] &] (* _Michael De Vlieger_, Dec 15 2019 *)
%o (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 (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 Cf. A288908 (with 1*log(P)), A330426 (with 2*log(P)), A330428 (Lowest Frogger Primes).
%K nonn
%O 1,1
%A _Steven M. Altschuld_, Dec 14 2019
%E More terms from _Michael De Vlieger_, Dec 15 2019
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