OFFSET
1,56
COMMENTS
Conjecture: a(n) > 0 for all n > 98.
We have verified this for n up to 36000.
The conjecture implies that there are infinitely many primes p with A047967(p) prime.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014
EXAMPLE
MATHEMATICA
pq[n_]:=PrimeQ[n]&&PrimeQ[PartitionsP[n]-PartitionsQ[n]]
f[n_, k_]:=EulerPhi[k]/2+EulerPhi[n-k]/12+1
a[n_]:=Sum[If[pq[f[n, k]], 1, 0], {k, 1, n-1}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 25 2014
STATUS
approved