OFFSET
1,4
COMMENTS
Conjecture: a(n) > 0 for all n > 3, and a(n) = 1 only for n = 5, 9, 25, 77, 104.
See also A237838 for a similar conjecture involving Sophie Germain primes.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..1100
EXAMPLE
a(9) = 1 since {p <= 4*9: p and p + 2 are both prime} = {3, 5, 11, 17, 29} has cardinality 5 and {5, 7} is a twin prime pair.
MATHEMATICA
TQ[n_]:=PrimeQ[n]&&PrimeQ[n+2]
tq[n_]:=Sum[If[PrimeQ[Prime[k]+2], 1, 0], {k, 1, PrimePi[n]}]
a[n_]:=Sum[If[TQ[tq[k*n]], 1, 0], {k, 1, n}]
Table[a[n], {n, 1, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 14 2014
STATUS
approved