[seqfan] Period lengths of k^2 mod n not in OEIS ?

Richard Mathar mathar at strw.leidenuniv.nl
Thu Feb 24 19:30:21 CET 2011

In conjunction with A182865 the following topic arose:

The sequence k^2 mod n for some fixed n has a period length not larger
than n (that is fundamental, k^2 is a polynomial...).
A000035 (n=2) had period 2,
A011655 (n=3) had period 3,
A000035 (again, n=4) has period 2,
A070430 (n=5) has period 5,
A070431 (n=6) has period 6,
A053879 (n=7) has period 7,
A070432 (n=8) has period 4,
A070433 (n=9) has period 9,
A008959 (n=10) has period 10,
A070434 (n=11) has period 11,
A070435, A070516 (n=12) has period 6
The number of different members in the period (set size of the moduli)
is A000224(n).

Now the strange thing is that these period lengths, 
seem not to be in the OEIS -- although they look even more fundamental than
the Pisano periods in my eyes. Am I fumbling somewhere here ?

Richard Mathar

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