A339625 - OEIS

%I #11 Dec 11 2020 03:35:34

%S 0,1,2,3,2,3,2,4,2,3,2,4,4,3,4,0,4,2,6,5,2,4,2,5,4,4,4,6,2,6,2,4,6,5,

%T 12,3,6,2,4,8,6,8,8,2,6,3,6,10,4,13,2,6,4,4,10,4,10,4,6,3,4,6,10,5,8,

%U 1,0,6,2,12,4,6,6,2,10,3,10,6,6,7,2,8,4,6,6,0,6,6,6,9,2,6,2,5,6,4

%N a(n) is the number of ways to write 6*n = p + q with p a lesser twin prime (A001359) and q a greater twin prime (A006512).

%C If 6*n = p + q, then also 6*n = (p+2) + (q-2), with p+2 a greater and q-2 a lesser twin prime. Thus a(n) is odd if and only if  n/2 is in A002822.

%H Robert Israel, <a href="/A339625/b339625.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4)=3 because 6*4 = 24 = 5 + 19 = 11 + 13 = 17 + 7 where (5,7), (11,13) and (17,19) are twin prime pairs.

%p N:= 600: # for a(1)..a(floor(N/6)))

%p P:= select(isprime, {seq(i,i=3..N,2)}):

%p T1:= sort(convert(P intersect map(`-`,P,2),list)):

%p T2:= map(`+`,T1,2):

%p V:= Vector(N):

%p nT:= nops(T1):

%p for i from 1 to nT do

%p   for j from 1 to nT do

%p     v:= T1[i]+T2[j];

%p     if v > N then break fi;

%p     V[v]:= V[v]+1;

%p od od:

%p seq(V[6*i],i=1..N/6);

%Y Cf. A001359, A006512, A002822, A339630.

%Y a(n)=0 for n in A243956.

%K nonn

%O 1,3

%A _J. M. Bergot_ and _Robert Israel_, Dec 10 2020