login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A198033
Greatest residue of x^n (mod 2n+1), x=0..2n.
2
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
0,2
COMMENTS
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, …
LINKS
EXAMPLE
a(10) = 18 because x^10 == 0, 1, 4, 7, 9, 15, 16, 18 (mod 21) => 18 is the greatest residue.
MATHEMATICA
Table[Max[Union[PowerMod[Range[0, 2*n], n, 2*n+1]]], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 20 2011
STATUS
approved