|
| |
|
|
A132385
|
|
Number of distinct primes among the cubes mod n.
|
|
0
| |
|
|
0, 0, 1, 1, 2, 3, 0, 3, 0, 4, 4, 4, 1, 2, 6, 5, 6, 1, 2, 7, 2, 8, 8, 8, 8, 2, 2, 2, 9, 10, 3, 10, 11, 11, 3, 2, 4, 5, 3, 11, 12, 4, 3, 13, 3, 14, 14, 14, 4, 14, 15, 4, 15, 4, 16, 5, 5, 16, 16, 16, 6, 6, 0, 17, 5, 18, 5, 18, 19, 5
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| This is to cubes A000578 as A132213 is to squares A000290.
It seems that the size of a(n) as compared to its surrounding elements is dependent on whether or not n is in A088232. If n is in A088232 the sequence assumes "big" values, otherwise the values will be "small". - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 24 2007
|
|
|
FORMULA
| a(n) = Card{p = k^3 mod n, for primes p and for all integers k}.
|
|
|
EXAMPLE
| a(10) = 4 because the cubes mod 10 repeat 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, ... of which the 4 distinct primes are {2, 3, 5, 7}.
|
|
|
MATHEMATICA
| Table[Length[Select[Union[Table[Mod[i^3, n], {i, 0, n}], Table[Mod[i^3, n], {i, 0, n}]], PrimeQ[ # ] &]], {n, 1, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 12 2007
|
|
|
CROSSREFS
| Cf. A000040, A000578, A132213.
Sequence in context: A160202 A195673 A128621 * A191716 A089235 A051910
Adjacent sequences: A132382 A132383 A132384 * A132386 A132387 A132388
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 07 2007
|
|
|
EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 12 2007
Spelling/notation corrections by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 18 2010
|
| |
|
|
