A070474 -id:A070474 - cp's OEIS frontend

A070597 Duplicate of A070474.

0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3

Offset: 0

N. J. A. Sloane, May 13 2002

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a(n)=A070474(n) [Proof: n^5-n^3 == 0 (mod 12) is shown explicitly for n=0 to 11, then the induction n->n+12 for the 5th-order polynomial followed by binomial expansion of (n+12)^k concludes that the zero (mod 12) is periodically extended to the other integers.] - R. J. Mathar, Jul 23 2009

Cf. A008960, A070474.

Table[Mod[n^5,12],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)

[power_mod(n,7,12) for n in range(0, 100)] # Zerinvary Lajos, Oct 28 2009

A070473 a(n) = n^3 mod 11.

Original entry on oeis.org

0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10

Offset: 0

N. J. A. Sloane, May 12 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A008960, A070474, A167176.

[n^3 mod 11: n in [0..80] ]; // Vincenzo Librandi, Jun 01 2011

Table[Mod[n^3,11],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,120],3,11] (* or *) PadRight[{},120,{0,1,8,5,9,4,7,2,6,3,10}] (* Harvey P. Dale, May 04 2019 *)

a(n)=n^3%11 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,3,11 ) for n in range(0, 99)] # Zerinvary Lajos, Oct 29 2009

a(n) = a(n-11). - G. C. Greubel, Mar 26 2016

A070516 Duplicate of A070435.

Original entry on oeis.org

0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4

Offset: 0

N. J. A. Sloane, May 13 2002

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n^4 mod 12 == A070435 n^2 mod 12 and both have the nice symmetrical cycle {0, 1, 4, 9, 4, 1, 0}. Also, A070597 n^5 mod 12 == A070474 n^3 mod 12 and both have the nice anti-symmetrical cycle {0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0}: a(i) + a(14-i) = 0 mod 12. - Zak Seidov, Feb 18 2006

Cf. A070435, A070474, A070597.

Table[Mod[n^4,12],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)

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A070597 Duplicate of A070474.

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A070473 a(n) = n^3 mod 11.

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A070516 Duplicate of A070435.

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