|
|
A331546
|
|
a(n) = |{k^(k+1)+(k+1)^k (mod prime(n)): k = 0..prime(n)-1}|.
|
|
1
|
|
|
1, 3, 5, 6, 7, 9, 11, 15, 15, 17, 19, 24, 25, 28, 28, 34, 39, 38, 41, 50, 43, 48, 55, 56, 60, 62, 70, 68, 70, 76, 76, 83, 83, 78, 88, 106, 95, 98, 105, 110, 117, 106, 114, 126, 114, 129, 138, 139, 143, 148, 146, 141, 152, 159, 164, 160, 170, 171, 176, 182, 184, 191, 192, 190, 193, 194, 216, 215, 215, 217
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Conjecture: |{k^(k+1)+(k+1)^k (mod p): k = 0..p-1}| = (1-1/e)*p + O(p^(1/2)), where p denotes a prime.
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 3 since {0^1+1^0, 1^2+2^1, 2^3+3^2} = {1, 3, 17} is a complete system of residues modulo the second prime 3.
|
|
MAPLE
|
f:= proc(p) local S, k;
nops({seq(k &^ (k+1) + (k+1) &^ k mod p, k=0..p-1)})
end proc:
|
|
MATHEMATICA
|
p[n_]:=p[n]=Prime[n];
a[n_]:=a[n]=Length[Union[Table[Mod[PowerMod[k, k+1, p[n]]+PowerMod[k+1, k, p[n]], p[n]], {k, 0, p[n]-1}]]];
Table[a[n], {n, 1, 70}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|