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.

Showing 1-3 of 3 results.

A049762 a(n) = Sum_{k=1..n} T(n,k), array T as in A049761.

Original entry on oeis.org

0, 0, 1, 1, 4, 1, 9, 7, 11, 12, 25, 18, 34, 34, 41, 32, 76, 44, 87, 64, 93, 85, 122, 75, 80, 160, 144, 132, 172, 103, 218, 232, 220, 245, 251, 210, 299, 330, 344, 315, 413, 275, 456, 392, 383, 472, 502, 479, 449, 553, 557, 626, 646, 632, 628, 618, 771
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Row sums of A049761.
Cf. A049759, A049760, A049763, A049764.

Programs

  • GAP
    List([1..60], n-> Sum([1..n], k-> PowerMod(n,3,k)) ); # G. C. Greubel, Dec 14 2019
  • Magma
    [&+[n^3 mod i: i in [1..n]]: n in [1..60]]; // Vincenzo Librandi, Sep 18 2017
  • Maple
    seq( add( `mod`(n^3, k), k = 1..n), n = 1..60); # G. C. Greubel, Dec 14 2019
  • Mathematica
    Table[Sum[Mod[n^3, i], {i, n}], {n, 60}] (* Vincenzo Librandi, Sep 18 2017 *)
  • PARI
    vector(60, n, sum(k=1,n, lift(Mod(n,k)^3)) ) \\ G. C. Greubel, Dec 14 2019
  • Sage
    [sum(power_mod(n,3,k) for k in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 14 2019

Formula

a(n) = Sum_{i=1..n} (n^3 mod i). - Wesley Ivan Hurt, Sep 15 2017

A049763 Triangular array T, read by rows: T(n,k) = n^4 mod k, for k = 1..n and n >= 1.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 4, 1, 0, 0, 1, 0, 1, 1, 3, 2, 1, 0, 0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 0, 1, 1, 1, 1, 1, 4, 1, 7, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 6, 1, 0, 0, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  0;
  0, 0;
  0, 1, 0;
  0, 0, 1, 0;
  0, 1, 1, 1, 0;
  0, 0, 0, 0, 1, 0;
  0, 1, 1, 1, 1, 1, 0;
  0, 0, 1, 0, 1, 4, 1, 0;
  0, 1, 0, 1, 1, 3, 2, 1, 0;
  0, 0, 1, 0, 0, 4, 4, 0, 1, 0;
  ...

Links

Crossrefs

Row sums are in A049764.
Cf. A049759, A049760, A049761, A049762.

Programs

  • GAP
    Flat(List([1..15], n-> List([1..n], k-> PowerMod(n,4,k) ))); # G. C. Greubel, Dec 13 2019
  • Magma
    [[Modexp(n,4,k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019
  • Maple
    seq(seq( `mod`(n^4, k), k = 1..n), n = 1..20); # G. C. Greubel, Dec 13 2019
  • Mathematica
    Flatten[Table[PowerMod[n,4,k],{n,20},{k,n}]] (* Harvey P. Dale, Jan 19 2015 *)
  • PARI
    T(n,k) = lift(Mod(n,k)^4);
for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 13 2019
  • Sage
    [[power_mod(n,4,k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019

A049769 Triangular array T read by rows: T(n,k) = (k^3 mod n) + (n^3 mod k).

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 1, 0, 4, 0, 1, 4, 4, 5, 0, 1, 2, 3, 4, 6, 0, 1, 2, 7, 4, 9, 7, 0, 1, 0, 5, 0, 7, 2, 8, 0, 1, 9, 0, 2, 12, 3, 2, 9, 0, 1, 8, 8, 4, 5, 10, 9, 2, 10, 0, 1, 9, 7, 12, 5, 12, 3, 9, 11, 11, 0, 1, 8, 3, 4, 8, 0, 13, 8, 9, 12, 12, 0
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			Triangle begins as:
  0;
  1, 0;
  1, 3, 0;
  1, 0, 4, 0;
  1, 4, 4, 5, 0;
  1, 2, 3, 4, 6, 0;
  1, 2, 7, 4, 9, 7, 0;
  1, 0, 5, 0, 7, 2, 8, 0;

Links

Crossrefs

Cf. A048154, A049761, A049767.

Programs

  • GAP
    Flat(List([1..15], n-> List([1..n], k-> PowerMod(k,3,n) + PowerMod(n,3,k) ))); # G. C. Greubel, Dec 13 2019
  • Magma
    [[Modexp(k,3,n) + Modexp(n,3,k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019
  • Maple
    seq(seq( `mod`(k^3, n) + `mod`(n^3, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019
  • Mathematica
    Table[PowerMod[k,3,n] + PowerMod[n,3,k], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)
  • PARI
    T(n,k) = lift(Mod(k,n)^3) + lift(Mod(n,k)^3);
for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 13 2019
  • Sage
    [[power_mod(k,3,n) + power_mod(n,3,k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019

Formula

T(n, k) = A048154(n, k) + A049761(n, k). - Michel Marcus, Dec 13 2019
Showing 1-3 of 3 results.

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