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

Author

Steven M. Altschuld, Dec 14 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

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

Programs

Magma

f:=func;  [p:p in PrimesUpTo(56000)|f(p)];// Marius A. Burtea, Dec 18 2019

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 *)

Extensions

More terms from Metin Sariyar, Dec 15 2019