A330426 Primes P where the distance to the nearest prime is greater than 2*log(P).

211, 2179, 2503, 3967, 4177, 7369, 7393, 11027, 11657, 14107, 16033, 16787, 18013, 18617, 18637, 18839, 19661, 21247, 23719, 24281, 29101, 32749, 33247, 33679, 33997, 37747, 38501, 40063, 40387, 42533, 42611, 44417, 46957, 51109, 51383, 53479, 54217, 55291, 55763

Offset

1,1

Comments

The author suggests that these numbers be called Double Frogger Primes because two 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..2000

Example

P = 211 is a term because 199 + 2*log(211) < 211 < 223 - 2*log(211).
P = 199 is not a term because 197 + 2*log(199) > 199.

Maple

q:= 3: state:= false: count:= 0: Res:= NULL:
while count < 100 do
  p:= nextprime(q);
  newstate:= is(p-q > 2*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

lst={}; Do[a=Prime[n]; If[Min[Abs[a-NextPrime[a, {-1, 1}]]]>2*Log[a], AppendTo[lst, a]], {n, 1, 10000}]; lst (* Metin Sariyar, Dec 15 2019 *)
(* Second program: *)
Select[Prime@ Range[10^4], Min@ Abs[# - NextPrime[#, {-1, 1}]] > 2 Log[#] &] (* Michael De Vlieger, Dec 15 2019 *)

Prog

(Magma) f:=func<p|Abs(p-NextPrime(p)) gt 2*Log(p) and Abs(p-PreviousPrime(p)) gt 2*Log(p)>;  [p:p in PrimesUpTo(56000)|f(p)]; // Marius A. Burtea, Dec 18 2019

Crossrefs

Cf. A288908 (with 1*log(P)), A330427 (with 3*log(P)), A330428.

Sequence in context: A108829 A111480 A291075 * A071367 A271979 A185719

Adjacent sequences: A330423 A330424 A330425 * A330427 A330428 A330429

Keyword

nonn

Author

Steven M. Altschuld, Dec 14 2019

Extensions

More terms from Metin Sariyar, Dec 15 2019

Status

approved