OFFSET
0,1
COMMENTS
Is this sequence finite?
The prime k-tuples conjecture implies that the sequence is infinite. - Robert Israel, Jul 11 2016
EXAMPLE
For j=0 a(0)=5 because 5-3 is prime.
For j=1 a(1)=8 because 8-5, 8-3 are all primes.
For j=2 a(2)=22 because 22-17, 22-5, 22-3 are all primes.
For j=3 a(3)=274 because 274-257, 274-17, 274-5, 274-3 are all primes.
MAPLE
f:= proc(n) local r, j, good;
for r from 2^(2^n)+4 by 2 do
good:= true;
for j from 0 to n do
if not isprime(r - 2^(2^j)-1) then good:= false; break fi
od;
if good then return(r) fi
od
end proc:
f(0):= 5:
map(f, [$0..5]); # Robert Israel, Jul 11 2016
PROG
(PARI) okprime(mink, vecf) = {for (i = 1, #vecf, if (! isprime(mink - vecf[i]), return (0)); ); return (1); }
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
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Felice Russo, Aug 29 2001
EXTENSIONS
18446744073810262144 from Thomas Baruchel, Oct 21 2003
STATUS
approved