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 1-5 of 5 results.

A365100 Number of distinct residues of x^n (mod n^3), x=0..n^3-1.

Original entry on oeis.org

1, 3, 7, 6, 21, 8, 43, 18, 55, 22, 111, 20, 157, 44, 147, 65, 273, 56, 343, 30, 105, 112, 507, 68, 501, 158, 487, 110, 813, 88, 931, 257, 777, 274, 903, 140, 1333, 344, 371, 102, 1641, 64, 1807, 280, 1155, 508, 2163, 260, 2059, 502, 1911, 200, 2757, 488, 483, 374, 805, 814
Offset: 1

Views

Author

Albert Mukovskiy, Aug 21 2023

Keywords

Crossrefs

Cf. A195637, A365099, A365101, A365102, A023105, A046631, A365103, A365104.

Programs

  • PARI
    a(n) = #Set(vector(n^3, x, Mod(x-1,n^3)^n)); \\ Michel Marcus, Aug 22 2023
  • Python
    def A365100(n): return len({pow(x,n,n**3) for x in range(n**3)}) # Chai Wah Wu, Aug 23 2023

A365101 Number of distinct residues of x^n (mod n^4), x=0..n^4-1.

Original entry on oeis.org

1, 4, 21, 18, 101, 30, 295, 130, 487, 153, 1211, 170, 2029, 444, 1919, 1025, 4625, 732, 6499, 442, 1881, 1818, 11639, 1290, 12501, 3045, 13123, 2516, 23549, 1530, 28831, 8193, 23009, 6939, 29795, 4148, 49285, 9750, 12863, 3354, 67241, 1500, 77659, 10302, 49187, 17460, 101615
Offset: 1

Views

Author

Albert Mukovskiy, Aug 21 2023

Keywords

Crossrefs

Cf. A195637, A365099, A365100, A365102, A023105, A046631, A365103, A365104.

Programs

  • PARI
    a(n) = #Set(vector(n^4, x, Mod(x-1,n^4)^n)); \\ Michel Marcus, Aug 22 2023
  • Python
    def A365101(n): return len({pow(x,n,n**4) for x in range(n**4)}) # Chai Wah Wu, Aug 23 2023

A365099 Number of distinct residues of x^n (mod n^2), x=0..n^2-1.

Original entry on oeis.org

1, 2, 3, 2, 5, 4, 7, 3, 7, 6, 11, 4, 13, 8, 15, 5, 17, 8, 19, 4, 9, 12, 23, 6, 21, 14, 19, 8, 29, 12, 31, 9, 33, 18, 35, 8, 37, 20, 15, 6, 41, 8, 43, 12, 35, 24, 47, 10, 43, 22, 51, 8, 53, 20, 15, 12, 21, 30, 59, 8, 61, 32, 21, 17, 65, 24, 67, 10, 69, 24, 71, 12, 73, 38, 63
Offset: 1

Views

Author

Albert Mukovskiy, Aug 21 2023

Keywords

Crossrefs

Cf. A195637, A365100, A365101, A365102, A023105, A046631, A365103.

Programs

  • PARI
    a(n) = #Set(vector(n^2, x, Mod(x-1,n^2)^n)); \\ Michel Marcus, Aug 22 2023
  • Python
    def A365099(n): return len({pow(x,n,n**2) for x in range(n**2)}) # Chai Wah Wu, Aug 22 2023

A365102 Number of distinct residues of x^n (mod n^5), x=0..n^5-1.

Original entry on oeis.org

1, 7, 57, 70, 501, 140, 2059, 1029, 4377, 1255, 13311, 1820, 26365, 5150, 27555, 16386, 78609, 10940, 123463, 8190, 37785, 33280, 267675, 28700, 312501, 65915, 354295, 66950, 682893, 35140, 893731, 262145, 732105, 196525, 1031559, 142220, 1823509, 308660
Offset: 1

Views

Author

Albert Mukovskiy, Aug 22 2023

Keywords

Crossrefs

Cf. A195637, A365099, A365100, A365101, A365103, A365104.

Programs

  • Mathematica
    a[n_]:=CountDistinct[Table[PowerMod[x-1,n,n^5],{x,0,n^5-1}]]; Array[a,38] (* Stefano Spezia, Aug 24 2023 *)
  • PARI
    a(n) = #Set(vector(n^5, x, Mod(x-1, n^5)^n));
  • Python
    def A365102(n): return len({pow(x,n,n**5) for x in range(n**5)}) # Chai Wah Wu, Aug 23 2023

A364811 Number of distinct residues x^4 (mod 2^n), x=0..2^n-1.

Original entry on oeis.org

1, 2, 2, 2, 2, 4, 6, 10, 18, 36, 70, 138, 274, 548, 1094, 2186, 4370, 8740, 17478, 34954, 69906, 139812, 279622, 559242, 1118482, 2236964, 4473926
Offset: 0

Views

Author

Albert Mukovskiy, Sep 14 2023

Keywords

Comments

For n>=4, A319281(a(n)) == 2^n + [(n mod 4)>0].
It appears that for n>4: a(n)=2*a(n-1)-2*[(n mod 4)==2]; a(n) = ceiling(2^n/15) - [(n mod 4)==0] + 1.

Crossrefs

Cf. A319281, A023105, A046630, A365103.

Programs

  • Mathematica
    a[n_]:=CountDistinct[Table[PowerMod[x-1, 4, 2^(n-1)], {x, 1, 2^(n-1)}]]; Array[a, 24]
  • PARI
    a(n) = #Set(vector(2^(n-1), x, Mod(x-1, 2^(n-1))^4))
  • Python
    def A364811(n): return len({pow(x,4,1<Chai Wah Wu, Sep 17 2023
Showing 1-5 of 5 results.

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