A070441 -id:A070441 - cp's OEIS frontend

A054580 n^2 modulo 17.

0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9

Offset: 0

Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 11 2000

Cf. A070439, A070440, A070441.

Table[Mod[n^2,17],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,90],2,17] (* Harvey P. Dale, Aug 16 2012 *)

a(n)=n^2%17 \\ Charles R Greathouse IV, Apr 06 2016

More terms from James Sellers, Apr 12 2000

A070440 a(n) = n^2 mod 18.

Original entry on oeis.org

0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9

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, 1).

Cf. A070441, A070442.

Table[Mod[n^2,18],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)

a(n)=n^2%18 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-18). - R. J. Mathar, Jul 27 2015

G.f.: -x*(1 +4*x +9*x^2 +16*x^3 +7*x^4 +13*x^6 +10*x^7 +9*x^8 +10*x^9 +13*x^10 +7*x^12 +16*x^13 +9*x^14 +4*x^15 +x^16) / ( (x-1)*(1+x+x^2)*(1+x^3+x^6)*(1+x)*(1-x+x^2)*(1-x^3+x^6) ). - R. J. Mathar, Jul 27 2015

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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A054580 n^2 modulo 17.

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A070440 a(n) = n^2 mod 18.

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

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