login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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(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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 04:56 EDT 2022. Contains 354048 sequences. (Running on oeis4.)