A339625 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).

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, 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, 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

Offset

1,3

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

N:= 600: # for a(1)..a(floor(N/6)))
P:= select(isprime, {seq(i, i=3..N, 2)}):
T1:= sort(convert(P intersect map(`-`, P, 2), list)):
T2:= map(`+`, T1, 2):
V:= Vector(N):
nT:= nops(T1):
for i from 1 to nT do
  for j from 1 to nT do
    v:= T1[i]+T2[j];
    if v > N then break fi;
    V[v]:= V[v]+1;
od od:
seq(V[6*i], i=1..N/6);

Crossrefs

Cf. A001359, A006512, A002822, A339630.

a(n)=0 for n in A243956.

Sequence in context: A007978 A245575 A333600 * A096737 A304535 A241856

Adjacent sequences: A339622 A339623 A339624 * A339626 A339627 A339628

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 10 2020

Status

approved