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 1-2 of 2 results.

A372905 Number of solutions for A330279 (numbers k such that x^k == k (mod k + 1) has multiple solutions for 0 <= x < k).

Original entry on oeis.org

2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 8, 2, 2, 6, 2, 2, 4, 2, 10, 2, 14, 2, 2, 2, 2, 2, 6, 8, 4, 8, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 14, 4, 2, 2, 26, 2, 6, 2, 2, 2, 2, 4, 2, 14, 2, 6, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 8, 38, 2, 2, 2, 10, 2, 4, 2, 2, 10, 4, 2
Offset: 1

Views

Author

Robert P. P. McKone, May 16 2024

Keywords

Crossrefs

Cf. A330279.

Programs

  • Mathematica
    Select[Table[Count[Table[PowerMod[x, k, k + 1], {x, 1, k - 1}], k], {k, 1, 813}], # >= 2 &]

A372771 Numbers m such that the congruence x^(m+1) == m (mod m+1) is solvable.

Original entry on oeis.org

1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 73, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 12 2024

Keywords

Comments

Includes all positive even numbers. - Robert Israel, Mar 14 2025

Examples

			9 is a term because x^(9+1) == 9 (mod 9+1) for x = 3 and x = 7, i.e., 3^10 = 59049 == 9 (mod 10) and 7^10 = 282475249 == 9 (mod 10).
		

Crossrefs

Programs

  • Maple
    select(m -> traperror(NumberTheory:-ModularRoot(m,m+1,m+1))::integer, [$1..200]); # Robert Israel, Mar 14 2025
  • Mathematica
    Select[Range[1, 110], With[{m = #}, AnyTrue[Range[1, m + 1], PowerMod[#, m + 1, m + 1] == m &]] &] (* Robert P. P. McKone, May 14 2024 *)

Extensions

Terms corrected by Robert P. P. McKone, May 14 2024
Showing 1-2 of 2 results.