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A330427
Primes P where the nearest prime is greater than 3*log(P) away.
4
38501, 58831, 153191, 203713, 206699, 232259, 247141, 250543, 268343, 279269, 286927, 302053, 330509, 362521, 362801, 404597, 413353, 421559, 430193, 438091, 479081, 479701, 485263, 504727, 512207, 515041, 539573, 539993, 546781, 569369, 574859, 590489, 624917
OFFSET
1,1
COMMENTS
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.
LINKS
MAPLE
q:= 3: state:= false: count:= 0: Res:= NULL:
while count < 100 do
p:= nextprime(q);
newstate:= is(p-q > 3*log(q));
if state and newstate then
count:= count+1; Res:= Res, q;
fi;
q:= p; state:= newstate;
od:
Res; # Robert Israel, Dec 18 2019
MATHEMATICA
Select[Prime@ Range[10^5], Min@ Abs[# - NextPrime[#, {-1, 1}]] > 3 Log[#] &] (* Michael De Vlieger, Dec 15 2019 *)
PROG
(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
(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
CROSSREFS
Cf. A288908 (with 1*log(P)), A330426 (with 2*log(P)), A330428 (Lowest Frogger Primes).
Sequence in context: A050766 A250712 A362217 * A289824 A321494 A252103
KEYWORD
nonn
AUTHOR
Steven M. Altschuld, Dec 14 2019
EXTENSIONS
More terms from Michael De Vlieger, Dec 15 2019
STATUS
approved