A010378 -id:A010378 - cp's OEIS frontend

A070438 a(n) = n^2 mod 15.

0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6

Offset: 0

N. J. A. Sloane, May 12 2002

Equivalently, n^6 mod 15. - Ray Chandler, Dec 27 2023

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

Cf. A000290, A008959, A010378, A070431, A070435, A070442, A070452, A159852.

Row 15 of A048152.

Table[Mod[n^2,15],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1},97] (* Ray Chandler, Aug 26 2015 *)

a(n)=n^2%15 \\ Charles R Greathouse IV, Sep 28 2015

[power_mod(n,2,15)for n in range(0, 97)] # Zerinvary Lajos, Nov 06 2009

From Reinhard Zumkeller, Apr 24 2009: (Start)
a(m*n) = a(m)*a(n) mod 15.
a(15*n+7+k) = a(15*n+8-k) for k <= 15*n+7.
a(15*n+k) = a(15*n-k) for k <= 15*n.
a(n+15) = a(n). (End)
From R. J. Mathar, Mar 14 2011: (Start)
a(n) = a(n-15).
G.f.: -x*(1+x) *(x^12+3*x^11+6*x^10-5*x^9+15*x^8-9*x^7+13*x^6-9*x^5+15*x^4-5*x^3+6*x^2+3*x+1) / ( (x-1) *(1+x^4+x^3+x^2+x) *(1+x+x^2) *(1-x+x^3-x^4+x^5-x^7+x^8) ). (End)
G.f.: (x^14 +4*x^13 +9*x^12 +x^11 +10*x^10 +6*x^9 +4*x^8 +4*x^7 +6*x^6 +10*x^5 +x^4 +9*x^3 +4*x^2 +x)/(-x^15 +1). - Colin Barker, Aug 14 2012

A010382 Squares mod 20.

Original entry on oeis.org

0, 1, 4, 5, 9, 16

Offset: 1

N. J. A. Sloane

Range of A070442. - Reinhard Zumkeller, Apr 24 2009

Cf. A010378, A010462, A010421. - Reinhard Zumkeller, Apr 24 2009
Row 20 of A096008.
Cf. A028733.

Union[PowerMod[Range[20], 2, 20]] (* Alonso del Arte, Dec 20 2019 *)

[quadratic_residues(20)] # Zerinvary Lajos, May 24 2009

(1 to 20).map(n => (n * n) % 20).toSet.toSeq.sorted // Alonso del Arte, Dec 20 2019

A010421 Squares mod 60.

Original entry on oeis.org

0, 1, 4, 9, 16, 21, 24, 25, 36, 40, 45, 49

Offset: 1

N. J. A. Sloane

Range of A159852. - Reinhard Zumkeller, Apr 24 2009

Cf. A010378, A010382, A010462. - Reinhard Zumkeller, Apr 24 2009
Row 60 of A096008.
Cf. A028773, A159852.

[n: n in [0..59] | IsSquare(R! n) where R:= ResidueClassRing(60)]; // Vincenzo Librandi, Jan 05 2020

Union[PowerMod[Range[60], 2, 60]] (* Alonso del Arte, Jan 03 2020 *)

[quadratic_residues(60)] # Zerinvary Lajos, May 24 2009

(1 to 60).map(n => n * n % 60).toSet.toSeq.sorted // Alonso del Arte, Jan 03 2020

A010462 Squares mod 30.

Original entry on oeis.org

0, 1, 4, 6, 9, 10, 15, 16, 19, 21, 24, 25

Offset: 1

N. J. A. Sloane

Range of A070452; a(k) + a(13-k) = 25, 1 <= k <= 12. - Reinhard Zumkeller, Apr 24 2009

			3^2 = 9, so 9 is in the sequence.
10^2 and 20^2 are both congruent to 10 mod 30, so 10 is in the sequence.
There are no solutions to x^2 = 11 mod 30, so 11 is not in the sequence.

Cf. A010378, A010382, A010421. - Reinhard Zumkeller, Apr 24 2009
Row 30 of A096008.
Cf. A028743.

Union[PowerMod[Range[30], 2, 30]] (* Alonso del Arte, Jan 30 2018 *)

[quadratic_residues(30)] # Zerinvary Lajos, May 24 2009

(1 to 30).map(n => n * n).map( % 30).toSet.toSeq.sorted // _Alonso del Arte, Nov 30 2019

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A070438 a(n) = n^2 mod 15.

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A010382 Squares mod 20.

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A010421 Squares mod 60.

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A010462 Squares mod 30.

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