OFFSET
1,10
COMMENTS
Conjecture: a(n) > 0 for all n > 7.
This implies that there are infinitely many primes p with p*(p+1) - prime(p) prime.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..5000
EXAMPLE
a(14) = 1 since 14 = 4 + 10 with prime(4) + phi(10) = 11 and 11*12 - prime(11) = 101 both prime.
a(15) = 1 since 15 = 6 + 9 with prime(6) + phi(9) = 19 and 19*20 - prime(19) = 313 both prime.
a(37) = 1 since 37 = 23 + 14 with prime(23) + phi(14) = 89 and 89*90 - prime(89) = 7549 both prime.
MATHEMATICA
PQ[n_]:=PrimeQ[n]&&PrimeQ[n(n+1)-Prime[n]]
f[n_, k_]:=Prime[k]+EulerPhi[n-k]
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 13 2014
STATUS
approved