OFFSET
1,4
COMMENTS
Conjectures:
(i) a(n) > 0 for all n > 2. Also, any integer n > 4 can be written as x + y (x, y > 0) with x^2 * y + 1 prime.
(ii) Each n = 2, 3, ... can be expressed as x + y (x, y > 0) with (x*y)^2 + x*y + 1 prime.
(iii) Also, any integer n > 2 can be written as x + y (x, y > 0) with 2*(x*y)^2 - 1 (or (x*y)^2 + x*y - 1) prime.
From Mauro Fiorentini, Jul 31 2023: (Start)
Both parts of conjecture (i) verified for n up to 10^9.
Conjecture (ii) and both parts of conjecture (iii) verified for n up to 10^7. (End)
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(6) = 1 since 6 = 4 + 2 with 4^2*2 - 1 = 31 prime.
MATHEMATICA
a[n_]:=Sum[If[PrimeQ[x^2*(n-x)-1], 1, 0], {x, 1, n-1}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Nov 12 2013
STATUS
approved