

A208643


Least positive integer m such that those k*(k1) mod m with k=1,...,n are pairwise distinct.


13



1, 3, 5, 7, 11, 11, 13, 16, 17, 19, 23, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 47, 47, 53, 53, 53, 59, 59, 59, 61, 64, 67, 67, 71, 71, 73, 79, 79, 79, 83, 83, 89, 89, 89, 97, 97, 97, 97, 101, 101, 103, 107, 107, 109, 113, 113, 127, 127, 127
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OFFSET

1,2


COMMENTS

On Feb. 29, 2012, ZhiWei Sun proved that a(n) = min{m>2n2: m is a prime or a power of two}. He also showed that if we replace k(k1) in the definition of a(n) by 2k(k1) then a(n) is the least prime greater than 2n2 for every n=2,3,4,....


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..500
ZhiWei Sun, A function taking only prime values, a message to Number Theory List, Feb. 21, 2012.
ZhiWei Sun, On functions taking only prime values, J. Number Theory 133(2013), no.8, 27942812.


MATHEMATICA

R[n_, i_] := Union[Table[Mod[k(k1), i], {k, 1, n}]]; Do[Do[If[Length[R[n, i]]==n, Print[n, " ", i]; Goto[aa]], {i, 1, 4n}]; Print[n]; Label[aa]; Continue, {n, 1, 1000}]


CROSSREFS

Cf. A000040, A207982, A208494.
Sequence in context: A066066 A241957 A112070 * A123252 A352185 A066168
Adjacent sequences: A208640 A208641 A208642 * A208644 A208645 A208646


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 29 2012


STATUS

approved



