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

1,1

Links

Table of n, a(n) for n=1..30.

Example

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.

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

Crossrefs

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

Sequence in context: A094849 A094852 A267543 * A058869 A054342 A216533

Adjacent sequences: A058864 A058865 A058866 * A058868 A058869 A058870

Keyword

nonn

Author

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

Extensions

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

Status

approved