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

0,1

Comments

Is this sequence finite?

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

Links

Table of n, a(n) for n=0..6.

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

Cf. A000215.

Sequence in context: A120041 A120042 A120043 * A092733 A116884 A192651

Adjacent sequences: A063894 A063895 A063896 * A063898 A063899 A063900

Keyword

hard,more,nonn

Author

Felice Russo, Aug 29 2001

Extensions

18446744073810262144 from Thomas Baruchel, Oct 21 2003

Status

approved