A236569 - OEIS

%I #6 Jan 29 2014 10:33:19

%S 0,0,3,3,3,5,3,3,5,3,3,5,3,5,11,3,3,5,31,3,5,3,3,5,3,5,11,3,5,31,3,3,

%T 5,31,3,5,3,3,5,43,3,5,3,5,11,3,5,43,31,3,5,3,3,5,3,3,5,3,5,11,43,11,

%U 43,31,3,5,3,5,11,3

%N Least term p of A236568 with 2*n - p prime, or 0 if such a prime p does not exist.

%C The conjecture in A236566 implies that a(n) > 0 for all n > 2.

%H Zhi-Wei Sun, <a href="/A236569/b236569.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 3 since prime(3 + 2) + 2 = 11 + 2 = 13 and 2*3 - 3 = 3 are both prime, but prime(2 + 2) + 2 = 9 is not.

%t p[m_]:=PrimeQ[Prime[m+2]+2]

%t Do[Do[If[p[Prime[k]]&&PrimeQ[2n-Prime[k]],Print[n," ",Prime[k]];Goto[aa]],{k,1,PrimePi[2n-1]}];

%t Print[n," ",0];Label[aa];Continue,{n,1,100}]

%Y Cf. A000040, A020481, A236566, A236568.

%K nonn

%O 1,3

%A _Zhi-Wei Sun_, Jan 29 2014