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

Author

Zhi-Wei Sun, Feb 29 2012

Keywords

• nonn

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.

Crossrefs

Cf. A000040, A207982, A208494.

Programs

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}]