A208643 Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct.

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

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: A066066 A241957 A112070 * A375345 A123252 A352185

Adjacent sequences: A208640 A208641 A208642 * A208644 A208645 A208646

Keyword

nonn

Author

Zhi-Wei Sun, Feb 29 2012

Status

approved