

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Robert Israel, Table of n, a(n) for n = 1..1000


MAPLE

q:= 3: state:= false: count:= 0: Res:= NULL:
while count < 100 do
p:= nextprime(q);
newstate:= is(pq > 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<pAbs(pNextPrime(p)) gt 3*Log(p) and Abs(pPreviousPrime(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(py, yx)>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: A013873 A050766 A250712 * A289824 A321494 A252103
Adjacent sequences: A330424 A330425 A330426 * A330428 A330429 A330430


KEYWORD

nonn


AUTHOR

Steven M. Altschuld, Dec 14 2019


EXTENSIONS

More terms from Michael De Vlieger, Dec 15 2019


STATUS

approved



