OFFSET
1,1
COMMENTS
Conjecture: all the terms are primes and a(n) < n^2 for all n > 1.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..258
Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012
Zhi-Wei Sun, A function taking only prime values, message to Number Theory List, Feb. 21, 2012.
Zhi-Wei Sun, On functions taking only prime values, J. Number Theory, Vol. 133, No. 8 (2013), pp. 2794-2812.
EXAMPLE
We have a(3)=5 since 2+2*3, 2+2*3*5, 2*3+2*3*5 are pairwise distinct modulo m=5 but not pairwise distinct modulo m=2,3,4.
MATHEMATICA
P[n_]:=Product[Prime[k], {k, 1, n}]
R[n_, m_]:=Product[If[Mod[P[k]+P[j], m]==0, 0, 1], {k, 2, n}, {j, 1, k-1}]
Do[Do[If[R[n, m]==1, Print[n, " ", m]; Goto[aa]], {m, 2, Max[2, n^2]}]; Print[n]; Label[aa]; Continue, {n, 1, 300}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Mar 18 2012
STATUS
approved