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