A070451 -id:A070451 - cp's OEIS frontend

A070456 a(n) = n^2 mod 34.

0, 1, 4, 9, 16, 25, 2, 15, 30, 13, 32, 19, 8, 33, 26, 21, 18, 17, 18, 21, 26, 33, 8, 19, 32, 13, 30, 15, 2, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 2, 15, 30, 13, 32, 19, 8, 33, 26, 21, 18, 17, 18, 21, 26, 33, 8, 19, 32, 13, 30, 15, 2, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 2, 15, 30

Offset: 0

N. J. A. Sloane, May 12 2002

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A070450, A070451, A070453.

Table[Mod[n^2,34],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)
PowerMod[Range[0,80],2,34] (* Harvey P. Dale, Mar 11 2023 *)

a(n)=n^2%34 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-34). - G. C. Greubel, Mar 25 2016

A070457 a(n) = n^2 mod 35.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 1, 14, 29, 11, 30, 16, 4, 29, 21, 15, 11, 9, 9, 11, 15, 21, 29, 4, 16, 30, 11, 29, 14, 1, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 1, 14, 29, 11, 30, 16, 4, 29, 21, 15, 11, 9, 9, 11, 15, 21, 29, 4, 16, 30, 11, 29, 14, 1, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 1, 14, 29, 11

Offset: 0

N. J. A. Sloane, May 12 2002

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A070450, A070451, A070453.

Table[Mod[n^2,35],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)
PowerMod[Range[0,80],2,35] (* Harvey P. Dale, Sep 07 2012 *)

a(n)=n^2%35 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-35). - G. C. Greubel, Mar 25 2016

A070453 a(n) = n^2 mod 31.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 5, 18, 2, 19, 7, 28, 20, 14, 10, 8, 8, 10, 14, 20, 28, 7, 19, 2, 18, 5, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 5, 18, 2, 19, 7, 28, 20, 14, 10, 8, 8, 10, 14, 20, 28, 7, 19, 2, 18, 5, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 5, 18, 2, 19, 7, 28, 20, 14, 10, 8, 8, 10, 14, 20

Offset: 0

N. J. A. Sloane, May 12 2002

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A070450, A070451.

Table[Mod[n^2,31],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)

a(n)=n^2%31 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-31). - G. C. Greubel, Mar 24 2016

A010391 Squares mod 29.

Original entry on oeis.org

0, 1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28

Offset: 1

N. J. A. Sloane

A070451 sorted, duplicates removed. - R. J. Mathar, Jan 12 2024

Cf. A010419, A028742.

Union[PowerMod[Range[29], 2, 29]] (* Alonso del Arte, Nov 29 2019 *)

[quadratic_residues(29)] # Zerinvary Lajos, May 24 2009

(1 to 29).map(n => n * n).map( % 29).toSet.toSeq.sorted // _Alonso del Arte, Nov 29 2019

A070454 a(n) = n^2 mod 32.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17

Offset: 0

N. J. A. Sloane, May 12 2002

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, 0, 1).

Cf. A070450, A070451, A070453.

Table[Mod[n^2,32],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)

a(n)=n^2%32 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-16). - G. C. Greubel, Mar 24 2016

A070455 a(n) = n^2 mod 33.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 3, 16, 31, 15, 1, 22, 12, 4, 31, 27, 25, 25, 27, 31, 4, 12, 22, 1, 15, 31, 16, 3, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 3, 16, 31, 15, 1, 22, 12, 4, 31, 27, 25, 25, 27, 31, 4, 12, 22, 1, 15, 31, 16, 3, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 3, 16, 31, 15, 1, 22, 12, 4

Offset: 0

N. J. A. Sloane, May 12 2002

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A070450, A070451, A070453.

Table[Mod[n^2,33],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)

a(n)=n^2%33 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-33). - G. C. Greubel, Mar 24 2016

A096459 Triangle read by rows: T(n,k) = n^2 mod prime(k), 1<=k<=n.

Original entry on oeis.org

1, 0, 1, 1, 0, 4, 0, 1, 1, 2, 1, 1, 0, 4, 3, 0, 0, 1, 1, 3, 10, 1, 1, 4, 0, 5, 10, 15, 0, 1, 4, 1, 9, 12, 13, 7, 1, 0, 1, 4, 4, 3, 13, 5, 12, 0, 1, 0, 2, 1, 9, 15, 5, 8, 13, 1, 1, 1, 2, 0, 4, 2, 7, 6, 5, 28, 0, 0, 4, 4, 1, 1, 8, 11, 6, 28, 20, 33, 1, 1, 4, 1, 4, 0, 16, 17, 8, 24, 14, 21, 5, 0, 1, 1, 0

Offset: 1

Reinhard Zumkeller, Aug 12 2004

T(n,k)=0 iff k is a prime factor of n:
A001221(n) = number of zeros in n-th row;
T(n,1)=A000035(n);
T(n,2)=A011655(n) for n>1; T(n,3)=A070430(n) for n>2;
T(n,4)=A053879(n) for n>3; T(n,5)=A070434(n) for n>4;
T(n,6)=A070436(n) for n>5; T(n,7)=A054580(n) for n>6;
T(n,8)=A070441(n) for n>7; T(n,9)=A070445(n) for n>8;
T(n,10)=A070451(n) for n>9;
T(n,n)=A069547(n).

			Triangle begins:
1;
0, 1;
1, 0, 4;
0, 1, 1, 2;
1, 1, 0, 4, 3;
0, 0, 1, 1, 3, 10;
1, 1, 4, 0, 5, 10, 15;
......

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A000290, A000040, A049759.

Table[Mod[n^2, Prime[k]], {n, 1, 10}, {k, 1, n}] (* G. C. Greubel, May 20 2017 *)

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A070456 a(n) = n^2 mod 34.

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A070457 a(n) = n^2 mod 35.

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A070453 a(n) = n^2 mod 31.

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A010391 Squares mod 29.

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A070454 a(n) = n^2 mod 32.

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A070455 a(n) = n^2 mod 33.

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A096459 Triangle read by rows: T(n,k) = n^2 mod prime(k), 1<=k<=n.

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