A200778 - OEIS

%I #24 Oct 24 2024 04:03:15

%S 2,1,5,1,2,3,3,13,9,8,10,43,69,15,17,50,3,42,1,2,3,3,20,33,3,44,7,35,

%T 49,9,6,189,15,1,113,21,7,154,3,3,18,12,29,33,20,6,27,3,2,3,23,11,10,

%U 12,18,137,41,12,36,29,54,17,10,59,55,3,51,36

%N Least k > 0 such that k*p*(k*p-1)-1 and k*p*(k*p-1)+1 is a twin prime pair, where p=prime(n).

%C Limit_{N->oo} (Sum_{n=1..N} k(n)) / (Sum_{n=1..N} log(p(n))^2) = 1.

%H Pierre CAMI, <a href="/A200778/b200778.txt">Table of n, a(n) for n = 1..10000</a>

%e 2*2*(2*2 - 1) - 1 = 11, twin prime of 13, so a(1)=2.

%p A200778 := proc(n)

%p     p := ithprime(n) ;

%p     for k from 1 do

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

%p             return k;

%p         end if;

%p     end do:

%p end proc:

%p seq(A200778(n),n=1..80) ; # _R. J. Mathar_, Nov 26 2011

%t lktpp[n_]:=Module[{k=1,p=Prime[n]},While[AnyTrue[k*p(k*p-1)+{1,-1}, CompositeQ],k++];k]; Array[lktpp,70] (* _Harvey P. Dale_, May 03 2019 *)

%Y Cf. A200654.

%K nonn

%O 1,1

%A _Pierre CAMI_, Nov 22 2011