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Search: id:A132385
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| A132385 |
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Number of distinct primes among the cubes mod n. |
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+0
1
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| 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; listen)
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OFFSET
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1,5
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COMMENT
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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 dependant 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
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FORMULA
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a(n) = Card{p = k^3 mod n, for primes p and for all integers k}.
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EXAMPLE
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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}.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A000040, A000578, A132213.
Sequence in context: A002708 A059283 A128621 this_sequence A089235 A051910 A137998
Adjacent sequences: A132382 A132383 A132384 this_sequence A132386 A132387 A132388
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 07 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 12 2007
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