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A208643 Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

On Feb. 29, 2012, Zhi-Wei Sun proved that a(n) = min{m>2n-2: m is a prime or a power of two}. He also showed that if we replace k(k-1) in the definition of a(n) by 2k(k-1) then a(n) is the least prime greater than 2n-2 for every n=2,3,4,....

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..500

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.

MATHEMATICA

R[n_, i_] := Union[Table[Mod[k(k-1), 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: A022457 A066066 A112070 * A123252 A066168 A215464

Adjacent sequences:  A208640 A208641 A208642 * A208644 A208645 A208646

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 29 2012

STATUS

approved

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Last modified July 31 19:47 EDT 2014. Contains 245087 sequences.