cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Reinhard Zumkeller, Mar 21 2010

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

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

Programs

Formula

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

Views

Author

N. J. A. Sloane

Keywords

Comments

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

Links

Crossrefs

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

Programs

Formula

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)

Extensions

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

A070436 a(n) = n^2 mod 13.

Original entry on oeis.org

0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4
Offset: 0

Views

Author

N. J. A. Sloane, May 12 2002

Keywords

Links

Crossrefs

Cf. A070434, A070435.

Programs

Formula

G.f.: (x^12 +4*x^11 +9*x^10 +3*x^9 +12*x^8 +10*x^7 +10*x^6 +12*x^5 +3*x^4 +9*x^3 +4*x^2 +x)/(-x^13 +1). - Colin Barker, Aug 14 2012
a(n) = a(n-13). - G. C. Greubel, Mar 24 2016

A070437 a(n) = n^2 mod 14.

Original entry on oeis.org

0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4, 1, 0, 1, 4, 9, 2, 11, 8, 7, 8, 11, 2, 9, 4
Offset: 0

Views

Author

N. J. A. Sloane, May 12 2002

Keywords

Links

Crossrefs

Cf. A070434, A070435, A070436.

Programs

Formula

G.f.: -x*(1 +4*x +9*x^2 +2*x^3 +11*x^4 +8*x^5 +7*x^6 +8*x^7 +11*x^8 +2*x^9 +9*x^10 +4*x^11 +x^12) / ((x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)). - R. J. Mathar, Jul 27 2015
a(n) = a(n-14). - G. C. Greubel, Mar 24 2016

A114448 Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 3, 4, 1, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 0, 0, 0, 2, 0, 5, 0, 0, 4, 1, 0, 1, 1, 1, 3, 1, 6, 1, 1, 9, 2, 1, 0, 0, 2, 0, 4, 4, 0, 0, 8, 6, 3, 4, 1, 0, 1, 0, 1, 0, 3, 1, 1, 0, 5, 4, 9, 2, 1
Offset: 1

Views

Author

Leroy Quet, Feb 14 2006

Keywords

Comments

Alternate description: triangular array a(n, k) = n^k (mod k) read by rows (n > 1, 0 < k < n). This is equivalent because a(n, k) = a(n-k, k). - David Wasserman, Jan 25 2007

Examples

			2^6 = 64 and 64 (mod 6) is 4. So a(2,6) = 4.

Crossrefs

Cf. A051127, A051128, A094263. Transpose of A060154. First 13 rows are A057427(n-1), A015910, A066601, A066602, A066603, A066604, A066438, A066439, A066440, A056969, A066441, A066442, A116609. First 12 columns are A000004, A000035, A010872, A000035, A010874, A070431, A010876, A000035, A021559(n+1), A008959, A010880, A070435.

Programs

  • Mathematica
    a[n_, k_] := Mod[n^k, k]; Table[a[n - k + 1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 12 2012 *)

Extensions

More terms from David Wasserman, Jan 25 2007
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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