A200653 - OEIS

%I #15 Apr 02 2024 03:01:13

%S 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,

%T 53,45,11,0,57,35,29,39,59,0,45,5,59,57,65,71,57,47,71,75,83,29,0,41,

%U 77,45,0,29,87,107,83,105,41,107,69,113,125,111,47,125

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

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

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

%H Pierre CAMI, <a href="/A200653/b200653.txt">Table of n, a(n) for n = 1..10000</a>

%p A200653 := proc(n)

%p     for k from 2*n-1 to -2 by -1 do

%p         if isprime(n*(n+1)+k) and isprime(n*(n+1)+k+2) then

%p             return k;

%p         end if;

%p     end do:

%p     return 0 ;

%p end proc:

%p seq(A200653(n),n=1..80) ; # _R. J. Mathar_, Nov 22 2011

%t 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 *)

%Y Cf. A200652.

%K sign

%O 1,3

%A _Pierre CAMI_, Nov 20 2011