A198020 -id:A198020 - cp's OEIS frontend

A198032 Numbers m such that the number of distinct residues of the congruence x^m (mod 2m+1) equals 2m+1, x=0..2m.

0, 1, 7, 17, 19, 25, 27, 43, 47, 55, 57, 59, 61, 71, 77, 79, 91, 93, 97, 101, 107, 109, 117, 127, 133, 143, 145, 147, 149, 151, 159, 161, 163, 167, 169, 177, 185, 195, 197, 199, 203, 205, 207, 223, 227, 235, 241, 257, 259, 263, 267, 271, 275, 277, 289, 291

Offset: 0

Michel Lagneau, Oct 20 2011

nonn

			a(2) = 7 because x^7  == 0, 1, ... 14  (mod 15) => 2*7+1 = 15 distinct residues.

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A198020, A197930.

lst:={};Table[If[Length[Union[PowerMod[Range[0,2*n],n,2*n+1]]]==2*n+1,AppendTo[lst,n]],{n,0,320}];lst

A198033 Greatest residue of x^n (mod 2n+1), x=0..2n.

Original entry on oeis.org

0, 2, 4, 6, 7, 10, 12, 14, 16, 18, 18, 22, 21, 26, 28, 30, 31, 34, 36, 38, 40, 42, 40, 46, 43, 50, 52, 54, 55, 58, 60, 62, 61, 66, 64, 70, 72, 74, 71, 78, 79, 82, 84, 86, 88, 90, 90, 94, 96, 98, 100, 102, 100, 106, 108, 110, 112, 114, 108, 118, 111, 122, 124

Offset: 0

Michel Lagneau, Oct 20 2011

nonn

If 2n+1 is prime, a(n) = 2n. But there exists nonprime numbers of the form 2n+1 such that a(n) = 2n, for example n = 0, 7, 13, 17, 19, 25, 27, 31, 37, 42, …

			a(10) = 18 because x^10 == 0, 1, 4, 7, 9, 15, 16, 18 (mod 21) => 18 is the greatest residue.

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A196082, A198020, A198032.

Table[Max[Union[PowerMod[Range[0,2*n],n,2*n+1]]],{n,0,100}]

cp's OEIS Frontend

A198032 Numbers m such that the number of distinct residues of the congruence x^m (mod 2m+1) equals 2m+1, x=0..2m.

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