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 A210144 a(n) = least integer m>1 such that the product of the first k primes for k=1,...,n are pairwise distinct modulo m. 8
 2, 3, 5, 11, 11, 23, 29, 37, 37, 41, 47, 47, 47, 47, 47, 73, 131, 131, 131, 131, 131, 151, 151, 151, 151, 199, 223, 223, 271, 271, 271, 281, 281, 281, 281, 281, 281, 281, 281, 281, 353, 353, 457, 457, 457, 457, 457, 457, 457, 457, 457, 641, 641, 641, 641, 641, 643, 643, 643, 643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: all the terms are primes and a(n) 1. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..1172 R. Mestrovic, 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, 2012 - From N. J. A. Sloane, Jun 13 2012 Zhi-Wei Sun,A function taking only prime values, a message to Number Theory List, Feb. 21, 2012. Zhi-Wei Sun, On functions taking only prime values, J. Number Theory 133(2013), no.8, 2794-2812. EXAMPLE a(3)=5 because 2, 2*3=6, 2*3*5=30 are distinct modulo m=5 but not distinct modulo m=2,3,4. MATHEMATICA R[n_, m_]:=Union[Table[Mod[Product[Prime[j], {j, 1, k}], m], {k, 1, n}]] Do[Do[If[Length[R[n, m]]==n, Print[n, " ", m]; Goto[aa]], {m, 2, Max[2, n^2]}]; Print[n]; Label[aa]; Continue, {n, 1, 1000}] CROSSREFS Cf. A000040, A207982, A208494, A208643. Sequence in context: A272197 A207982 A259155 * A243357 A066159 A316794 Adjacent sequences:  A210141 A210142 A210143 * A210145 A210146 A210147 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 17 2012 STATUS approved

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Last modified May 28 01:34 EDT 2020. Contains 334671 sequences. (Running on oeis4.)