A163111 Prime numbers with gaps larger than 18 towards both neighboring primes.

3967, 11027, 11657, 14107, 16033, 16787, 18013, 18617, 18637, 18839, 19661, 21247, 23719, 24281, 24571, 29101, 30367, 31357, 32749, 33247, 33679, 33997, 35201, 36037, 37747, 38501, 40063, 40387, 42533, 42611, 43691, 43913, 44417, 46957

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 20 2009

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for primes, gaps between

Crossrefs

Cf. A137875, A137874, A137873, A137872, A137871

Programs

Mathematica

lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4]&&!PrimeQ[p-6]&&!PrimeQ[p+6]&& !PrimeQ[p-8]&&!PrimeQ[p+8]&&!PrimeQ[p-10]&&!PrimeQ[p+10]&&!PrimeQ[p-12]&&!PrimeQ[p+12]&&!PrimeQ[p-14]&&!PrimeQ[p+14]&&!PrimeQ[p-16]&&!PrimeQ[p+16]&&!PrimeQ[p-18]&&!PrimeQ[p+18], AppendTo[lst,p]],{n,8!}];lst
Select[Partition[Prime[Range[5000]],3,1],Min[Differences[#]]>18&][[All,2]] (* Harvey P. Dale, Jul 08 2021 *)

Formula

{A000040(i) : A001223(i) > 18 and A001223(i-1) > 18}. - R. J. Mathar, Jul 27 2009

Extensions

Definition rephrased by R. J. Mathar, Jul 27 2009