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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.

%I A058867 #18 Sep 25 2015 10:33:16
%S A058867 5,53,211,16787,69623,247141,3565979,4911311,12012743,23346809,
%T A058867 34346287,36598607,51042053,383204683,4470608101,5007182863,
%U A058867 5558570491,48287689717,50284155289,178796541817,264860525507,374787490919,1521870804107,2093308790851,4228611064537,6537587646671,17432065861517,22546768250359,26923643849953,187891466722913
%N 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.
%e A058867 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.
%p A058867 Primes:= select(isprime,[2,seq(2*i+1,i=1..10^7)]):
%p A058867 g:= 0: count:= 0:
%p A058867 for i from 2 to nops(Primes)-1 do
%p A058867   if Primes[i+1]+Primes[i-1] = 2*Primes[i] and Primes[i+1]-Primes[i] > g then
%p A058867      count:= count+1;
%p A058867      a[count]:= Primes[i];
%p A058867      g:= Primes[i+1]-Primes[i];
%p A058867   fi
%p A058867 od:
%p A058867 seq(a[i],i=1..count); # _Robert Israel_, Sep 20 2015
%Y A058867 The distances are in A058868. First occurrences of distances are in A054342.
%K A058867 nonn
%O A058867 1,1
%A A058867 Harvey Dubner (harvey(AT)dubner.com), Dec 07 2000; extended Sep 11 2004
%E A058867 a(21)-a(30) from _Dmitry Petukhov_, Sep 22 2015