A200652 a(n) = least k with -3<k<2*n such that n*(n+1)+k and n*(n+1)+k+2 are twin primes, or 0 if no such k exists.

1, -1, -1, 0, -1, -1, 3, -1, 11, 0, 5, 23, 9, 17, -1, 9, 5, 5, 0, -1, -1, 15, 17, -1, 9, 0, 53, 9, 11, 0, 27, 5, 29, 39, 17, 0, 21, -1, 47, 27, -1, 65, 39, 17, 11, 75, 11, 29, 0, -1, 5, 33, 0, -1, 39, 59, 23, 39, -1, 11, 39, 11, 17, 57, 47, -1, 81, 29, 101, 39, 119, 23, 15, 89, 41

Offset

1,7

Comments

Only 11 values are zero for n < 434. Conjecture: no more 0 values if n>433.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Maple

A200652 := proc(n)
    for k from -2 to 2*n-1 do
        if isprime(n*(n+1)+k) and isprime(n*(n+1)+k+2) then
            return k;
        end if;
    end do:
    return 0 ;
end proc:
seq(A200652(n), n=1..80) ; # R. J. Mathar, Nov 22 2011

Mathematica

a[n_]:=Module[{k=0}, For[m=-2, m<2n&&k==0, m++, If[PrimeQ[n(n+1)+m]&&PrimeQ[n(n+1)+m+2], k=m]]; k]; Array[a, 75] (* Stefano Spezia, Apr 01 2024 *)

Crossrefs

Cf. A200653.

Sequence in context: A210725 A048953 A358987 * A276391 A119632 A201131

Adjacent sequences: A200649 A200650 A200651 * A200653 A200654 A200655

Keyword

sign

Author

Pierre CAMI, Nov 20 2011

Status

approved