A058867 Equidistant lonely primes. Each prime is the same distance (gap) from the preceding prime and the next prime. These distances are maximal: each distance is larger than all such previous distances.

5, 53, 211, 16787, 69623, 247141, 3565979, 4911311, 12012743, 23346809, 34346287, 36598607, 51042053, 383204683, 4470608101, 5007182863, 5558570491, 48287689717, 50284155289, 178796541817, 264860525507, 374787490919, 1521870804107, 2093308790851, 4228611064537, 6537587646671, 17432065861517, 22546768250359, 26923643849953, 187891466722913

Offset: 1

Author

Harvey Dubner (harvey(AT)dubner.com), Dec 07 2000; extended Sep 11 2004

Keywords

• nonn

Examples

			47, 53 and 59 are primes. There are no other primes between 47 and 59 and 59-53=53-47=6. There are no other such primes with a smaller distance so 53 is included in the sequence.
		

Crossrefs

The distances are in A058868. First occurrences of distances are in A054342.

Programs

Maple

Primes:= select(isprime,[2,seq(2*i+1,i=1..10^7)]):
g:= 0: count:= 0:
for i from 2 to nops(Primes)-1 do
  if Primes[i+1]+Primes[i-1] = 2*Primes[i] and Primes[i+1]-Primes[i] > g then
     count:= count+1;
     a[count]:= Primes[i];
     g:= Primes[i+1]-Primes[i];
  fi
od:
seq(a[i],i=1..count); # Robert Israel, Sep 20 2015

Extensions

a(21)-a(30) from Dmitry Petukhov, Sep 22 2015