A070438 -id:A070438 - cp's OEIS frontend

A070638 Duplicate of A070438.

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 13 2002

dead

A008959 Final digit of squares: a(n) = n^2 mod 10.

Original entry on oeis.org

0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0

Offset: 0

N. J. A. Sloane, Mar 15 1996

a(m*n) = a(m)*a(n) mod 10; a(5*n+k) = a(5*n-k) for k <= 5*n. - Reinhard Zumkeller, Apr 24 2009
a(n) = n^6 mod 10. - Zerinvary Lajos, Nov 06 2009
a(n) = A002015(n) mod 10 = A174452(n) mod 10. - Reinhard Zumkeller, Mar 21 2010
Decimal expansion of 166285490/1111111111. - Alexander R. Povolotsky, Mar 09 2013

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for sequences related to final digits of numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Cf. A000290, A070431, A070435, A070438, A070442, A070452, A159852, A010879, A008960, A070514.

[0] cat [Intseq(n^2)[1]: n in [1..80]]; // Bruno Berselli, Feb 14 2013

[n^2 - 10*Floor(n^2/10): n in [0..80]]; // Vincenzo Librandi, Jun 16 2015

A008959:=n->(n^2 mod 10); seq(A008959(n), n=0..50); # Wesley Ivan Hurt, Jun 06 2014

Table[Mod[n^2,10],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
PowerMod[Range[0,80],2,10] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,0,1},{0,1,4,9,6,5,6,9,4,1},120] (* Harvey P. Dale, Oct 16 2012 *)

a(n)=n^2%10 \\ Charles R Greathouse IV, Sep 24 2015

[power_mod(n,2,10) for n in range(0, 81)] # Zerinvary Lajos, Nov 06 2009

Periodic with period 10. - Franklin T. Adams-Watters, Mar 13 2006
a(n) = 4.5 - (1 + 5^(1/2))*cos(Pi*n/5) + (-1 - 3/5*5^(1/2))*cos(2*Pi*n/5) + (5^(1/2) - 1)*cos(3*Pi*n/5) + (-1 + 3/5*5^(1/2))*cos(4*Pi*n/5) - 0.5*(-1)^n. - Richard Choulet, Dec 12 2008
a(n) = A010879(A000290(n)). - Reinhard Zumkeller, Jan 04 2009
G.f.: (x^9+4*x^8+9*x^7+6*x^6+5*x^5+6*x^4+9*x^3+4*x^2+x)/(-x^10+1). - Colin Barker, Aug 14 2012
a(n) = n^2 - 10*floor(n^2/10). - Wesley Ivan Hurt, Jun 12 2013
a(n) = (n - 5*A002266(n + 2))^2 + 5*(5*A002266(n + 2) mod 2). - Wesley Ivan Hurt, Jun 06 2014
a(n) = A033569(n+3) mod 10. - Wesley Ivan Hurt, Dec 06 2014
a(n) = n^k mod 10; for k > 0 where k mod 4 = 2. - Doug Bell, Jun 15 2015

A070431 a(n) = n^2 mod 6.

Original entry on oeis.org

0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4

Offset: 0

N. J. A. Sloane, May 12 2002

a(m*n) = a(m)*a(n) mod 6; a(3*n+k) = a(3*n-k) for k <= 3*n. - Reinhard Zumkeller, Apr 24 2009
Equivalently n^6 mod 6. - Zerinvary Lajos, Nov 06 2009
Equivalently: n^(2*m + 4) mod 6; n^(2*m + 2) mod 6. - G. C. Greubel, Apr 01 2016

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).

Cf. A000290, A008959, A070435, A070438, A070442, A070452, A159852.

[n^2 mod 6 : n in [0..100]]; // Wesley Ivan Hurt, Apr 01 2016

[Modexp(n, 2, 6): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016

A070431:=n->n^2 mod 6: seq(A070431(n), n=0..100); # Wesley Ivan Hurt, Apr 01 2016

Table[Mod[n^2, 6], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1},{0, 1, 4, 3, 4, 1},101] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,120],2,6] (* or *) PadRight[{},120,{0,1,4,3,4,1}] (* Harvey P. Dale, Aug 11 2019 *)

a(n)=n^2%6 \\ Charles R Greathouse IV, Sep 24 2015

[power_mod(n,2,6) for n in range(0, 101)] # Zerinvary Lajos, Oct 30 2009

G.f.: -x*(1+4*x+3*x^2+4*x^3+x^4)/((x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)). - R. J. Mathar, Jul 23 2009
a(n) = a(n-6). - Reinhard Zumkeller, Apr 24 2009
From G. C. Greubel, Apr 01 2016: (Start)
a(6*m) = 0.
a(2*n) = 4*A011655(n).
a(n) = (1/6)*(13 + 3*(-1)^n - 12*cos(n*Pi/3) - 4*cos(2*n*Pi/3)).
G.f.: (x +4*x^2 +3*x^3 + 4*x^4 +x^5)/(1 - x^6). (End)

A048152 Triangular array T read by rows: T(n,k) = k^2 mod n, for 1 <= k <= n, n >= 1.

Original entry on oeis.org

0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 4, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 2, 2, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0

Offset: 1

Clark Kimberling

			Rows:
  0;
  1, 0;
  1, 1, 0;
  1, 0, 1, 0;
  1, 4, 4, 1, 0;
  1, 4, 3, 4, 1, 0;

T. D. Noe, Rows n = 1..100 of triangle, flattened
Eric Weisstein's World of Mathematics, Quadratic Residue

Cf. A060036.
Cf. A225126 (central terms).
Cf. A070430 (row 5), A070431 (row 6), A053879 (row 7), A070432 (row 8), A008959 (row 10), A070435 (row 12), A070438 (row 15), A070422 (row 20).
Cf. A046071 (in ascending order, without zeros and duplicates).
Cf. A063987 (for primes, in ascending order, without zeros and duplicates).

a048152 n k = a048152_tabl !! (n-1) !! (k-1)
a048152_row n = a048152_tabl !! (n-1)
a048152_tabl = zipWith (map . flip mod) [1..] a133819_tabl
-- Reinhard Zumkeller, Apr 29 2013

Flatten[Table[PowerMod[k,2,n],{n,15},{k,n}]] (* Harvey P. Dale, Jun 20 2011 *)

T(n,k) = A133819(n,k) mod n, k = 1..n. - Reinhard Zumkeller, Apr 29 2013

T(n,k) = (T(n,k-1) + (2k+1)) mod n. - Andrés Ventas, Apr 06 2021

A070435 a(n) = n^2 mod 12, or alternately n^4 mod 12.

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 12 2002

Period 6: repeat [0,1,4,9,4,1].
Occurs in Mariotte reference, pp. 511-512. Consider waterjets of heights 0,5,10, ... = A008587 up to 100 pieds (feet). a(n) is the difference in pouces (inches) between tank's heights (in feet and inches) and part in feet (0,5,10,15,21,..). Row with 0's is implicit. - Paul Curtz, Nov 18 2008
a(m*n) = a(m)*a(n) mod 12; a(6*n+k) = a(6*n-k) for k <= 6*n. - Reinhard Zumkeller, Apr 24 2009
n^z mod 12, if z even number. Example: n^180 mod 12. etc... - Zerinvary Lajos, Nov 06 2009
Equivalently: n^(2*m + 2) mod 12. - G. C. Greubel, Apr 01 2016

Edme Mariotte, Règles pour les jets d'eau, pp. 508-518. In Divers ouvrages de mathématique et de physique par Messieurs de l'Académie Royale des Sciences, 6, 518, 1 p., Paris, 1693. Edme Mariotte (1620-1684) is known for the perfect gas law (1676, Essai sur l'air), but later than Robert Boyle (1662). - Paul Curtz, Nov 18 2008

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A000290, A008959, A070431, A070438, A070442, A070452, A159852, A260686.

[Modexp(n, 2, 12): n in [0..100]]; // Wesley Ivan Hurt, Apr 01 2016

A070435:=n->n^2 mod 12: seq(A070435(n), n=0..100); # Wesley Ivan Hurt, Apr 01 2016

Table[Mod[n^2,12],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1},{0, 1, 4, 9, 4, 1},101] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0, 100], 2, 12] (* Wesley Ivan Hurt, Apr 02 2016 *)

a(n)=n^2%12 \\ Charles R Greathouse IV, Sep 23 2013

[power_mod(n,4,12) for n in range(0, 101)] # Zerinvary Lajos, Oct 31 2009

G.f.: x*(1 + 4*x + 9*x^2 + 4*x^3 + x^4)/((1 - x)*(1 + x)*(1 + x + x^2)*(1 - x + x^2)). - R. J. Mathar, Jul 23 2009
a(n) = (1/6)*(19 - 3*(-1)^n - 24*cos(n*Pi/3) + 8*cos(2*n*Pi/3)). - G. C. Greubel, Apr 01 2016
a(n) = A260686(n)^2. - Wesley Ivan Hurt, Apr 01 2016

Incorrect g.f. removed by Georg Fischer, May 15 2019

A070442 a(n) = n^2 mod 20.

Original entry on oeis.org

0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16

Offset: 0

N. J. A. Sloane, May 12 2002

Also, n^6 mod 20.

Equivalently n^10 mod 20. - Zerinvary Lajos, Oct 31 2009

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

Cf. A000290, A008959, A010382, A070431, A070435, A070438, A070452, A159852.

Row 20 of A048152.

Table[Mod[n^2,20],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 1, 4, 9, 16, 5, 16, 9, 4, 1},95] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,100],2,20] (* or *) PadRight[{},120,{0,1,4,9,16,5,16,9,4,1}] (* Harvey P. Dale, Jan 06 2019 *)

a(n)=n^2%20 \\ Charles R Greathouse IV, Jun 11 2015

[power_mod(n,10,20) for n in range(0, 88)] # Zerinvary Lajos, Oct 31 2009

From Reinhard Zumkeller, Apr 24 2009: (Start)
a(m*n) = a(m)*a(n) mod 20.
a(5*n+k) = a(5*n-k) for k <= 5*n.
a(n+10) = a(n). (End)
G.f. -x*(1+4*x+9*x^2+16*x^3+5*x^4+16*x^5+9*x^6+4*x^7+x^8) / ( (x-1) *(1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) ). - R. J. Mathar, Aug 27 2013

A070452 a(n) = n^2 mod 30.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, May 12 2002

Equivalently, n^6 mod 30. - 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 (-1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1).

A010462, A070431, A008959, A070435, A070438, A070442, A159852, A000290. - Reinhard Zumkeller, Apr 24 2009

Table[Mod[n^2,30],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)
LinearRecurrence[{-1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1},{0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9},80] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,80],6,30] (* or *) PadRight[{},80,{0,1,4,9,16,25,6,19,4,21,10,1,24,19,16,15,16,19,24,1,10,21,4,19,6,25,16,9,4,1}] (* Harvey P. Dale, Jul 10 2023 *)

a(n)=n^2%30 \\ Charles R Greathouse IV, Oct 07 2015

[power_mod(n,2,30)for n in range(0, 75)] # Zerinvary Lajos, Nov 03 2009

From Reinhard Zumkeller, Apr 24 2009: (Start)
a(m*n) = a(m)*a(n) mod 30.
a(15*n+k) = a(15*n-k) for k<=15*n.
a(n+30) = a(n). (End)
a(n)= -a(n-1) +a(n-3) +a(n-4) -a(n-6) -a(n-7) +a(n-9) +a(n-10) -a(n-12) -a(n-13) +a(n-15) +a(n-16) -a(n-18) -a(n-19) +a(n-21) +a(n-22) -a(n-24) -a(n-25) +a(n-27) +a(n-28). - R. J. Mathar, Jul 23 2009

A159852 n^2 mod 60.

Original entry on oeis.org

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

Offset: 0

Reinhard Zumkeller, Apr 24 2009

Periodic with period 30: a(n+30) = a(n);
a(15*n+k) = a(15*n-k) for k<=15*n;
a(m*n) = a(m)*a(n) mod 60;
A010421 gives the range of this sequence.

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, 1).

Cf. A070431, A008959, A070435, A070438, A070442, A070452, A000290.

LinearRecurrence[{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},{0, 1, 4, 9, 16, 25, 36, 49, 4, 21, 40, 1, 24, 49, 16, 45, 16, 49, 24, 1, 40, 21, 4, 49, 36, 25, 16, 9, 4, 1},80] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,80],2,60] (* or *) PadRight[{},80,{0,1,4,9,16,25,36,49,4,21,40,1,24,49,16,45,16,49,24,1,40,21,4,49,36,25,16,9,4,1}] (* Harvey P. Dale, Jun 19 2018 *)

a(n)=n^2%60 \\ Charles R Greathouse IV, May 09 2013

A174452 a(n) = n^2 mod 1000.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 24, 89, 156, 225, 296, 369, 444, 521, 600, 681, 764, 849, 936, 25, 116, 209, 304, 401, 500, 601, 704, 809, 916, 25

Offset: 0

Reinhard Zumkeller, Mar 21 2010

a(n) = A000290(n) for n < 32, but a(32) = 24;
A008959(n) = a(n) mod 10; A002015(n) = a(n) mod 100;
periodic with period 500: a(n+500)=a(n) and a(250*n+k)=a(250*n-k) for k <= 250*n;
a(n) = (n mod 1000)^2 mod 1000;
a(m*n) = a(m)*a(n) mod 1000;
A122986 gives the range of this sequence;
a(n) = n for n = 0, 1, and 376.

			Some calculations for n=982451653, to be realized by hand:
a(n) = (53^2 + 200*6*3) mod 1000 = 6409 mod 1000 = 409;
a(n) = (653^2) mod 1000 = 426409 mod 1000 = 409;
a(n) = a(n mod 500) = a(153) = 409;
a(n) = 965211250482432409 mod 1000 = 409.

Cf. A053879, A070430, A070431, A070432, A070433, A070434, A070435, A070438, A070442, A070452, A159852.

a174452 = (`mod` 1000) . (^ 2)  -- Reinhard Zumkeller, Jul 06 2011

seq(n^2 mod 1000, n=0..55); # Nathaniel Johnston, Jun 22 2011

PowerMod[Range[0,60],2,1000] (* Harvey P. Dale, Feb 08 2022 *)

a(n)=n^2%1000 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = ((n mod 100)^2 + 200 * (floor(n/100) mod 10) * (n mod 10)) mod 1000.

A002015 a(n) = n^2 reduced mod 100.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81

Offset: 0

N. J. A. Sloane

Periodic with period 50: (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1) and next term is 0. The period is symmetrical about the "midpoint" 25. - Zak Seidov, Oct 26 2009

A010461 gives the range of this sequence. - Reinhard Zumkeller, Mar 21 2010

Index entries for sequences related to final digits of numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,1).

Cf. A053879, A070430, A070431, A070432, A070433, A070434, A070435, A070438, A070442, A070452, A159852.

PowerMod[Range[0,60],2,100] (* Harvey P. Dale, Nov 28 2012 *)

a(n)=n^2%100 \\ Charles R Greathouse IV, Oct 07 2015

From Reinhard Zumkeller, Mar 21 2010: (Start)
a(n) = (n mod 10) * ((n mod 10) + 20 * ((n\10) mod 10)) mod 100.
a(n) = A174452(n) mod 100; A008959(n) = a(n) mod 10;
a(m*n) = a(m)*a(n) mod 100;
a(n) = (n mod 100)^2 mod 100;
a(n) = n for n = 0, 1, and 25. (End)

Definition rephrased at the suggestion of Zak Seidov, Oct 26 2009

cp's OEIS Frontend

A070638 Duplicate of A070438.

Views

Author

Keywords

A008959 Final digit of squares: a(n) = n^2 mod 10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Magma

Maple

Mathematica

PARI

Sage

Formula

A070431 a(n) = n^2 mod 6.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Magma

Maple

Mathematica

PARI

Sage

Formula

A048152 Triangular array T read by rows: T(n,k) = k^2 mod n, for 1 <= k <= n, n >= 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

A070435 a(n) = n^2 mod 12, or alternately n^4 mod 12.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions

A070442 a(n) = n^2 mod 20.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

A070452 a(n) = n^2 mod 30.

Views

Author

Keywords

Comments

Links