User talk:M. F. Hasler/Periodic sequences of the form m^n mod p

Many sequences of the form "Period P : repeat (a,b,...,z)" are also of the form a(n)=m^n mod p (where mod = pmod in Maple syntax). I don't know if there are is an index for these, so I made one on my own: see /Periodic sequences of the form m^n mod p:

{forprime(p=3,20,print1("\n p="p);for(m=2,p-1,s=m;
for(i=2,80,#s<80|break;s=Str(s","m^i%p)); print1("\n\t m="m": http://oeis.org/search?q=",s)))}

 p=3
A000034 m=2: http://oeis.org/search?q=2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2
 p=5
A070402 m=2: http://oeis.org/search?q=2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1,2
A070352 m=3: http://oeis.org/search?q=3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3,4,2,1,3
A010685 m=4: http://oeis.org/search?q=4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4
 p=7
A069705 m=2: http://oeis.org/search?q=2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4
A033940 m=3: http://oeis.org/search?q=3,2,6,4,5,1,3,2,6,4,5,1,3,2,6,4,5,1,3,2,6,4,5,1,3,2,6,4,5,1,3,2,6,4,5,1,3,2,6,4,5
A153727 m=4: http://oeis.org/search?q=4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2
A070365 m=5: http://oeis.org/search?q=5,4,6,2,3,1,5,4,6,2,3,1,5,4,6,2,3,1,5,4,6,2,3,1,5,4,6,2,3,1,5,4,6,2,3,1,5,4,6,2,3
A010687 m=6: http://oeis.org/search?q=6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6
 p=11
A036117 m=2: http://oeis.org/search?q=2,4,8,5,10,9,7,3,6,1,2,4,8,5,10,9,7,3,6,1,2,4,8,5,10,9,7,3,6,1,2,4,8,5,10,9,7,3,6
A070341 m=3: http://oeis.org/search?q=3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3,9,5,4,1,3
A168429 m=4: http://oeis.org/search?q=4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4,5,9,3,1,4
A070367 m=5: http://oeis.org/search?q=5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5,3,4,9,1,5
A070392 m=6: http://oeis.org/search?q=6,3,7,9,10,5,8,4,2,1,6,3,7,9,10,5,8,4,2,1,6,3,7,9,10,5,8,4,2,1,6,3,7,9,10,5,8,4,2
A070404 m=7: http://oeis.org/search?q=7,5,2,3,10,4,6,9,8,1,7,5,2,3,10,4,6,9,8,1,7,5,2,3,10,4,6,9,8,1,7,5,2,3,10,4,6,9,8
A048271 m=8: http://oeis.org/search?q=8,9,6,4,10,3,2,5,7,1,8,9,6,4,10,3,2,5,7,1,8,9,6,4,10,3,2,5,7,1,8,9,6,4,10,3,2,5,7
A187466 m=9: http://oeis.org/search?q=9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9,4,3,5,1,9
A010691 m=10: http://oeis.org/search?q=10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10
 p=13
A036118 m=2: http://oeis.org/search?q=2,4,8,3,6,12,11,9,5,10,7,1,2,4,8,3,6,12,11,9,5,10,7,1,2,4,8,3,6,12,11,9,5,10,7,1
        m=3: http://oeis.org/search?q=3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9,1,3,9
        m=4: http://oeis.org/search?q=4,3,12,9,10,1,4,3,12,9,10,1,4,3,12,9,10,1,4,3,12,9,10,1,4,3,12,9,10,1,4,3,12,9,10
        m=5: http://oeis.org/search?q=5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1
A070393 m=6: http://oeis.org/search?q=6,10,8,9,2,12,7,3,5,4,11,1,6,10,8,9,2,12,7,3,5,4,11,1,6,10,8,9,2,12,7,3,5,4,11,1
A070405 m=7: http://oeis.org/search?q=7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1
        m=8: http://oeis.org/search?q=8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1,8,12,5,1
        m=9: http://oeis.org/search?q=9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3
        m=10: http://oeis.org/search?q=10,9,12,3,4,1,10,9,12,3,4,1,10,9,12,3,4,1,10,9,12,3,4,1,10,9,12,3,4,1,10,9,12,3,4
        m=11: http://oeis.org/search?q=11,4,5,3,7,12,2,9,8,10,6,1,11,4,5,3,7,12,2,9,8,10,6,1,11,4,5,3,7,12,2,9,8,10,6,1
        m=12: http://oeis.org/search?q=12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12
 p=17
        m=2: http://oeis.org/search?q=2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8
        m=3: http://oeis.org/search?q=3,9,10,13,5,15,11,16,14,8,7,4,12,2,6,1,3,9,10,13,5,15,11,16,14,8,7,4,12,2,6,1,3,9
        m=4: http://oeis.org/search?q=4,16,13,1,4,16,13,1,4,16,13,1,4,16,13,1,4,16,13,1,4,16,13,1,4,16,13,1,4,16,13,1,4
        m=5: http://oeis.org/search?q=5,8,6,13,14,2,10,16,12,9,11,4,3,15,7,1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7,1,5,8
A070394 m=6: http://oeis.org/search?q=6,2,12,4,7,8,14,16,11,15,5,13,10,9,3,1,6,2,12,4,7,8,14,16,11,15,5,13,10,9,3,1,6,2
        m=7: http://oeis.org/search?q=7,15,3,4,11,9,12,16,10,2,14,13,6,8,5,1,7,15,3,4,11,9,12,16,10,2,14,13,6,8,5,1,7,15
        m=8: http://oeis.org/search?q=8,13,2,16,9,4,15,1,8,13,2,16,9,4,15,1,8,13,2,16,9,4,15,1,8,13,2,16,9,4,15,1,8,13
        m=9: http://oeis.org/search?q=9,13,15,16,8,4,2,1,9,13,15,16,8,4,2,1,9,13,15,16,8,4,2,1,9,13,15,16,8,4,2,1,9,13
       m=10: http://oeis.org/search?q=10,15,14,4,6,9,5,16,7,2,3,13,11,8,12,1,10,15,14,4,6,9,5,16,7,2,3,13,11,8,12,1,10
       m=11: http://oeis.org/search?q=11,2,5,4,10,8,3,16,6,15,12,13,7,9,14,1,11,2,5,4,10,8,3,16,6,15,12,13,7,9,14,1,11
       m=12: http://oeis.org/search?q=12,8,11,13,3,2,7,16,5,9,6,4,14,15,10,1,12,8,11,13,3,2,7,16,5,9,6,4,14,15,10,1,12
       m=13: http://oeis.org/search?q=13,16,4,1,13,16,4,1,13,16,4,1,13,16,4,1,13,16,4,1,13,16,4,1,13,16,4,1,13,16,4,1,13
       m=14: http://oeis.org/search?q=14,9,7,13,12,15,6,16,3,8,10,4,5,2,11,1,14,9,7,13,12,15,6,16,3,8,10,4,5,2,11,1,14
       m=15: http://oeis.org/search?q=15,4,9,16,2,13,8,1,15,4,9,16,2,13,8,1,15,4,9,16,2,13,8,1,15,4,9,16,2,13,8,1,15,4
       m=16: http://oeis.org/search?q=16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16,1,16
 p=19
A036120 m=2: http://oeis.org/search?q=2,4,8,16,13,7,14,9,18,17,15,11,3,6,12,5,10,1,2,4,8,16,13,7,14,9,18,17,15,11,3,6,12
A070342 m=3: http://oeis.org/search?q=3,9,8,5,15,7,2,6,18,16,10,11,14,4,12,17,13,1,3,9,8,5,15,7,2,6,18,16,10,11,14,4,12
A187532 m=4: http://oeis.org/search?q=4,16,7,9,17,11,6,5,1,4,16,7,9,17,11,6,5,1,4,16,7,9,17,11,6,5,1,4,16,7,9,17,11,6,5
A070373 m=5: http://oeis.org/search?q=5,6,11,17,9,7,16,4,1,5,6,11,17,9,7,16,4,1,5,6,11,17,9,7,16,4,1,5,6,11,17,9,7,16,4
A070395 m=6: http://oeis.org/search?q=6,17,7,4,5,11,9,16,1,6,17,7,4,5,11,9,16,1,6,17,7,4,5,11,9,16,1,6,17,7,4,5,11,9,16
A070421 m=7: http://oeis.org/search?q=7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11
        m=8: http://oeis.org/search?q=8,7,18,11,12,1,8,7,18,11,12,1,8,7,18,11,12,1,8,7,18,11,12,1,8,7,18,11,12,1,8,7,18
        m=9: http://oeis.org/search?q=9,5,7,6,16,11,4,17,1,9,5,7,6,16,11,4,17,1,9,5,7,6,16,11,4,17,1,9,5,7,6,16,11,4,17
        m=10: http://oeis.org/search?q=10,5,12,6,3,11,15,17,18,9,14,7,13,16,8,4,2,1,10,5,12,6,3,11,15,17,18,9,14,7,13,16
        m=11: http://oeis.org/search?q=11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7,1,11,7
        m=12: http://oeis.org/search?q=12,11,18,7,8,1,12,11,18,7,8,1,12,11,18,7,8,1,12,11,18,7,8,1,12,11,18,7,8,1,12,11
        m=13: http://oeis.org/search?q=13,17,12,4,14,11,10,16,18,6,2,7,15,5,8,9,3,1,13,17,12,4,14,11,10,16,18,6,2,7,15,5
        m=14: http://oeis.org/search?q=14,6,8,17,10,7,3,4,18,5,13,11,2,9,12,16,15,1,14,6,8,17,10,7,3,4,18,5,13,11,2,9,12
        m=15: http://oeis.org/search?q=15,16,12,9,2,11,13,5,18,4,3,7,10,17,8,6,14,1,15,16,12,9,2,11,13,5,18,4,3,7,10,17
        m=16: http://oeis.org/search?q=16,9,11,5,4,7,17,6,1,16,9,11,5,4,7,17,6,1,16,9,11,5,4,7,17,6,1,16,9,11,5,4,7,17,6
        m=17: http://oeis.org/search?q=17,4,11,16,6,7,5,9,1,17,4,11,16,6,7,5,9,1,17,4,11,16,6,7,5,9,1,17,4,11,16,6,7,5,9
        m=18: http://oeis.org/search?q=18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18

As can be seen from the m=6 lines, e.g., some of these have been submitted in another grouping:

A070392 - A070395 = 6^n mod p=11,13,...,19.

— M. F. Hasler 18:51, 10 March 2011 (UTC)