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A063897 a(n) is the least k such that k - A000215(j), j=0..n, are all primes.

%I A063897 #14 Jul 11 2016 22:40:02
%S A063897 5,8,22,274,65704,4295145556,18446744073810262144
%N A063897 a(n) is the least k such that k - A000215(j), j=0..n, are all primes.
%C A063897 Is this sequence finite?
%C A063897 The prime k-tuples conjecture implies that the sequence is infinite. - _Robert Israel_, Jul 11 2016
%e A063897 For j=0 a(0)=5 because 5-3 is prime.
%e A063897 For j=1 a(1)=8 because 8-5, 8-3 are all primes.
%e A063897 For j=2 a(2)=22 because 22-17, 22-5, 22-3 are all primes.
%e A063897 For j=3 a(3)=274 because 274-257, 274-17, 274-5, 274-3 are all primes.
%p A063897 f:= proc(n) local r, j, good;
%p A063897     for r from 2^(2^n)+4 by 2 do
%p A063897        good:= true;
%p A063897        for j from 0 to n do
%p A063897           if not isprime(r - 2^(2^j)-1) then good:= false; break fi
%p A063897        od;
%p A063897        if good then return(r) fi
%p A063897     od
%p A063897 end proc:
%p A063897 f(0):= 5:
%p A063897 map(f, [$0..5]); # _Robert Israel_, Jul 11 2016
%o A063897 (PARI) okprime(mink, vecf) = {for (i = 1, #vecf, if (! isprime(mink - vecf[i]), return (0));); return (1);}
%o A063897 a(n) = {mink = 2^(2^n) + 2; vecf = vector(n+1, i, 2^(2^(i-1)) + 1); while (! okprime(mink, vecf), mink++); mink;} \\ _Michel Marcus_, Sep 28 2013
%Y A063897 Cf. A000215.
%K A063897 hard,more,nonn
%O A063897 0,1
%A A063897 _Felice Russo_, Aug 29 2001
%E A063897 18446744073810262144 from _Thomas Baruchel_, Oct 21 2003