OFFSET
1,5
COMMENTS
Conjecture: a(n) > 0 for all n > 712.
This implies the conjecture in A236566.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(100) = 1 since 100 = 10 + 90 with 2*10 + phi(90) - 1 = 20 + 24 - 1 = 43, prime(43 + 2) + 2 = 197 + 2 = 199 and 2*100 - 43 = 157 all prime.
a(1727) = 1 since 1727 = 956 + 771 with 2*956 + phi(771) - 1 = 1912 + 512 - 1 = 2423, prime(2423 + 2) + 2 = 21599 + 2 = 21601 and 2*1727 - 2423 = 1031 all prime.
MATHEMATICA
p[n_]:=PrimeQ[n]&&PrimeQ[Prime[n+2]+2]
f[n_, k_]:=2k+EulerPhi[n-k]-1
a[n_]:=Sum[If[p[f[n, k]]&&PrimeQ[2n-f[n, k]], 1, 0], {k, 1, n-1}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 29 2014
STATUS
approved