A063898 - OEIS

%I #10 Sep 28 2013 08:08:36

%S 2,2,2,14,14,14,66746,475424,12124166,14899339904

%N Smallest k > 0 such that k + F_n are all primes, where F_n is the n-th Fermat number.

%C Is this sequence finite?

%e For j=3 a(3)=2 because 257+2, 17+2, 5+2, 3+2 are all primes.

%e For j=4 a(4)=14 because 65537+14, 257+14, 17+14, 5+14, 3+14 are all primes.

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

%o a(n) = {mink = 1; vecf = vector(n+1, i, 2^(2^(i-1)) + 1); while (! okprimep(mink, vecf), mink++); mink;} \\ _Michel Marcus_, Sep 28 2013

%Y Cf. A000215 (Fermat numbers).

%K hard,more,nonn

%O 0,1

%A _Felice Russo_, Aug 29 2001

%E a(10) from _Donovan Johnson_, Oct 12 2008