A200653 a(n) = greatest k with -3<k<2*n such that n*(n+1)+k and n*(n+1)+k+2 are twin primes.

1, -1, 5, 0, -1, -1, 3, -1, 17, 0, 17, 23, 15, 17, 29, 9, 5, 5, 0, 11, -1, 15, 17, 41, 9, 0, 53, 45, 11, 0, 57, 35, 29, 39, 59, 0, 45, 5, 59, 57, 65, 71, 57, 47, 71, 75, 83, 29, 0, 41, 77, 45, 0, 29, 87, 107, 83, 105, 41, 107, 69, 113, 125, 111, 47, 125

Offset

1,3

Comments

There are only 11 0 values for n<434, and no more 0 values for n>433.

If n>433, a(n) is > A200652.

Links

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

Maple

A200653 := proc(n)
    for k from 2*n-1 to -2 by -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(A200653(n), n=1..80) ; # R. J. Mathar, Nov 22 2011

Mathematica

a[n_]:=Module[{k=0}, For[m=-2, m<2n, m++, If[PrimeQ[n(n+1)+m]&&PrimeQ[n(n+1)+m+2], k=m]]; k]; Array[a, 66] (* Stefano Spezia, Apr 01 2024 *)

Crossrefs

Cf. A200652.

Sequence in context: A199916 A363041 A180494 * A058064 A316568 A198927

Adjacent sequences: A200650 A200651 A200652 * A200654 A200655 A200656

Keyword

sign

Author

Pierre CAMI, Nov 20 2011

Status

approved