A063897 - OEIS

%I #14 Jul 11 2016 22:40:02

%S 5,8,22,274,65704,4295145556,18446744073810262144

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

%C Is this sequence finite?

%C The prime k-tuples conjecture implies that the sequence is infinite. - _Robert Israel_, Jul 11 2016

%e For j=0 a(0)=5 because 5-3 is prime.

%e For j=1 a(1)=8 because 8-5, 8-3 are all primes.

%e For j=2 a(2)=22 because 22-17, 22-5, 22-3 are all primes.

%e For j=3 a(3)=274 because 274-257, 274-17, 274-5, 274-3 are all primes.

%p f:= proc(n) local r, j, good;

%p     for r from 2^(2^n)+4 by 2 do

%p        good:= true;

%p        for j from 0 to n do

%p           if not isprime(r - 2^(2^j)-1) then good:= false; break fi

%p        od;

%p        if good then return(r) fi

%p     od

%p end proc:

%p f(0):= 5:

%p map(f, [$0..5]); # _Robert Israel_, Jul 11 2016

%o (PARI) okprime(mink, vecf) = {for (i = 1, #vecf, if (! isprime(mink - vecf[i]), return (0));); return (1);}

%o 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 Cf. A000215.

%K hard,more,nonn

%O 0,1

%A _Felice Russo_, Aug 29 2001

%E 18446744073810262144 from _Thomas Baruchel_, Oct 21 2003