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 A210186 a(n) = least integer m>1 such that m divides none of P_i + P_j with 0
 2, 3, 5, 7, 11, 19, 23, 23, 23, 47, 59, 61, 71, 71, 71, 101, 101, 101, 101, 101, 101, 113, 113, 113, 113, 113, 113, 113, 113, 113, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 487, 487, 661, 661, 661, 661, 661, 661, 661, 661, 661, 719, 719, 719, 719, 719, 719, 811, 811, 811, 811, 811, 811, 811, 811, 811, 811 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000040, A210144, A208494, A208643, A207982. Sequence in context: A069749 A081889 A078139 * A120628 A322471 A262837 Adjacent sequences:  A210183 A210184 A210185 * A210187 A210188 A210189 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 18 2012 STATUS approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)