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A330427
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Primes P where the nearest prime is greater than 3*log(P) away.
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4
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MAPLE
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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:
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MATHEMATICA
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Select[Prime@ Range[10^5], Min@ Abs[# - NextPrime[#, {-1, 1}]] > 3 Log[#] &] (* Michael De Vlieger, Dec 15 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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