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A109746 Number of unique sequences of the type m^k mod n for n fixed, k>=1. 0
1, 2, 3, 4, 2, 6, 4, 7, 4, 10, 3, 12, 6 (list; graph; refs; listen; history; internal format)
OFFSET

2,2

COMMENTS

It appears that a(p)= p-1 (for prime p) and a(2p) = p-1 (for odd prime p), but this is only speculation. I (or someone else) need to calculate more values of a(n) to settle this conjecture.

EXAMPLE

E.g.: m mod 4 = {0,1,2,3,0,1,2,3,...}; m^2 mod 4 = {0,1,0,1,...}; m^3 mod 4= {0,1,0,3,0,1,0,3,...}; but m^4 mod 4 = {0,1,0,1} = m^2 mod 4; so for higher powers of m these sequences cycle and are not unique, thus for mod 4 we have {0,1,2,3}, {0,1} and {0,1,0,3} as unique and a(4) = 3

CROSSREFS

Sequence in context: A120636 A117744 A091732 * A061020 A206369 A178970

Adjacent sequences:  A109743 A109744 A109745 * A109747 A109748 A109749

KEYWORD

nonn

AUTHOR

Bruce Corrigan (scentman(AT)myfamily.com), Aug 10 2005

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Last modified February 14 01:35 EST 2012. Contains 205567 sequences.