A205321 Smallest k>=0 such that (2^n+k)*2^n-1 and (2^n+k)*2^n+1 are a twin prime pair.

0, 11, 1, 11, 4, 11, 13, 116, 34, 14, 241, 44, 97, 458, 337, 59, 604, 206, 67, 167, 424, 179, 97, 326, 259, 284, 1177, 77, 328, 356, 508, 74, 1798, 749, 2197, 1289, 643, 839, 1171, 1427, 814, 2564, 31, 4244, 379, 5099, 3706, 4871, 2719, 3194, 7057, 122, 5329, 2636, 301, 2852, 3793

Offset: 1

Author

Pierre CAMI, Jul 14 2012

Keywords

• nonn

Comments

Conjecture : there is at least one k for each n.

Links

• Pierre CAMI, Table of n, a(n) for n = 1..825

Crossrefs

Cf. A191617, A191618, A205322

Programs

Maple

A205321 := proc(n)
    local a,p ;
    for a from 0 do
         p := (2^n+a)*2^n-1 ;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 18 2012

Formula

a(n) = A082466(2^n), n>1. - R. J. Mathar, Jul 20 2012