OFFSET
1,5
COMMENTS
Conjecture: a(n) > 0 for all n > 3.
This is stronger than Goldbach's weak conjecture which was finally proved by H. A. Helfgott in 2013.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..5000
H. A. Helfgott, Minor arcs for Goldbach's problem, arXiv:1205.5252 [math.NT], 2012-2013.
H. A. Helfgott, Major arcs for Goldbach's theorem, arXiv:1305.2897 [math.NT], 2013-2014.
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014-2016.
EXAMPLE
MATHEMATICA
p[n_]:=PrimeQ[Prime[n]-n+1]
q[n_]:=PrimeQ[n]&&p[n]
a[n_]:=Sum[If[p[Prime[i]]&&p[Prime[j]]&&q[2n-1-Prime[i]-Prime[j]], 1, 0], {i, 1, PrimePi[(2n-1)/3]}, {j, i, PrimePi[(2n-1-Prime[i])/2]}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 31 2014
STATUS
approved