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 1-4 of 4 results.

A341410 a(n) = (Sum_{k=1..4} k^n) mod n.

Original entry on oeis.org

0, 0, 1, 2, 0, 0, 3, 2, 1, 0, 10, 6, 10, 2, 10, 2, 10, 12, 10, 14, 16, 8, 10, 18, 0, 4, 1, 18, 10, 0, 10, 2, 1, 30, 5, 30, 10, 30, 22, 34, 10, 18, 10, 2, 10, 30, 10, 18, 31, 0, 49, 42, 10, 30, 35, 2, 43, 30, 10, 54, 10, 30, 37, 2, 0, 6, 10, 14, 31, 60, 10, 66, 10, 30
Offset: 1

Views

Author

Seiichi Manyama, Feb 11 2021

Keywords

Crossrefs

(Sum_{k=1..m} k^n) mod n: A096196 (m=2), A341409 (m=3), this sequence (m=4), A341411 (m=5), A341412 (m=6), A341413 (m=7).

Programs

  • Maple
    a:= n-> add(i&^n, i=1..4) mod n:
    seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021
  • Mathematica
    a[n_] := Mod[Sum[k^n, {k, 1, 4}], n]; Array[a, 100] (* Amiram Eldar, Feb 11 2021 *)
  • PARI
    a(n) = sum(k=1, 4, k^n)%n;

Formula

a(n) = A001551(n) mod n.
a(A056643(n)) = 0.

A341411 a(n) = (Sum_{k=1..5} k^n) mod n.

Original entry on oeis.org

0, 1, 0, 3, 0, 1, 1, 3, 0, 5, 4, 7, 2, 13, 0, 3, 15, 13, 15, 19, 15, 11, 15, 19, 0, 3, 0, 27, 15, 25, 15, 3, 27, 21, 15, 31, 15, 17, 30, 19, 15, 19, 15, 11, 0, 9, 15, 19, 1, 25, 21, 43, 15, 31, 25, 27, 54, 55, 15, 19, 15, 55, 36, 3, 5, 55, 15, 27, 18, 55, 15, 67, 15, 55
Offset: 1

Views

Author

Seiichi Manyama, Feb 11 2021

Keywords

Crossrefs

(Sum_{k=1..m} k^n) mod n: A096196 (m=2), A341409 (m=3), A341410 (m=4), this sequence (m=5), A341412 (m=6), A341413 (m=7).

Programs

  • Maple
    a:= n-> add(i&^n, i=1..5) mod n:
    seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021
  • Mathematica
    a[n_] := Mod[Sum[k^n, {k, 1, 5}], n]; Array[a, 100] (* Amiram Eldar, Feb 11 2021 *)
  • PARI
    a(n) = sum(k=1, 5, k^n)%n;

Formula

a(n) = A001552(n) mod n.
a(A056741(n)) = 0.

A341412 a(n) = (Sum_{k=1..6} k^n) mod n.

Original entry on oeis.org

0, 1, 0, 3, 1, 1, 0, 3, 0, 1, 10, 7, 8, 7, 6, 3, 4, 13, 2, 15, 0, 3, 21, 19, 1, 13, 0, 7, 21, 1, 21, 3, 12, 23, 21, 31, 21, 15, 12, 35, 21, 13, 21, 31, 36, 45, 21, 19, 0, 1, 33, 39, 21, 31, 46, 35, 42, 33, 21, 55, 21, 29, 0, 3, 46, 49, 21, 31, 27, 21, 21, 67, 21, 17
Offset: 1

Views

Author

Seiichi Manyama, Feb 11 2021

Keywords

Crossrefs

(Sum_{k=1..m} k^n) mod n: A096196 (m=2), A341409 (m=3), A341410 (m=4), A341411 (m=5), this sequence (m=6), A341413 (m=7).

Programs

  • Maple
    a:= n-> add(i&^n, i=1..6) mod n:
    seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021
  • Mathematica
    a[n_] := Mod[Sum[k^n, {k, 1, 6}], n]; Array[a, 100] (* Amiram Eldar, Feb 11 2021 *)
    Table[Mod[Total[Range[6]^n],n],{n,100}] (* Harvey P. Dale, Dec 02 2023 *)
  • PARI
    a(n) = sum(k=1, 6, k^n)%n;

Formula

a(n) = A001553(n) mod n.
a(A056745(n)) = 0.

A341413 a(n) = (Sum_{k=1..7} k^n) mod n.

Original entry on oeis.org

0, 0, 1, 0, 3, 2, 0, 4, 1, 0, 6, 8, 2, 0, 4, 4, 11, 14, 9, 16, 7, 8, 5, 20, 8, 10, 1, 0, 28, 20, 28, 4, 25, 4, 14, 32, 28, 26, 4, 36, 28, 20, 28, 12, 28, 2, 28, 20, 0, 0, 19, 48, 28, 32, 34, 28, 43, 24, 28, 56, 28, 16, 28, 4, 18, 20, 28, 52, 25, 0, 28, 68, 28, 66, 19, 40
Offset: 1

Views

Author

Seiichi Manyama, Feb 11 2021

Keywords

Crossrefs

(Sum_{k=1..m} k^n) mod n: A096196 (m=2), A341409 (m=3), A341410 (m=4), A341411 (m=5), A341412 (m=6), this sequence (m=7).

Programs

  • Maple
    a:= n-> add(i&^n, i=1..7) mod n:
    seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021
  • Mathematica
    a[n_] := Mod[Sum[k^n, {k, 1, 7}], n]; Array[a, 100] (* Amiram Eldar, Feb 11 2021 *)
  • PARI
    a(n) = sum(k=1, 7, k^n)%n;

Formula

a(n) = A001554(n) mod n.
a(A056750(n)) = 0.
From Robert Israel, Feb 09 2023: (Start)
Given positive integer k, let m = A001554(k).
If p is a prime > m/k and A001554(p*k) == m (mod k), then a(p*k) = m.
This is true for all primes p > m/k for k = 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, ...
For k = 5 or 15 it is true for primes p > m/k with p == 1 (mod 4).
For k = 11 it is true for primes p > m/k with p == 1 or 7 (mod 10).
For k = 13 it is true for primes p > m/k with p == 1 (mod 12).
(End)
Showing 1-4 of 4 results.