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

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

Offset: 0

Author

Felice Russo, Aug 29 2001

Keywords

• hard
• more
• nonn

Comments

Is this sequence finite?

The prime k-tuples conjecture implies that the sequence is infinite. - Robert Israel, Jul 11 2016

Examples

			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.
		

Crossrefs

Cf. A000215.

Programs

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

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

Extensions

18446744073810262144 from Thomas Baruchel, Oct 21 2003