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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.

User: Ethan E. Wood

Ethan E. Wood's wiki page.

Ethan E. Wood has authored 2 sequences.

A380036 Smallest number which is not a triangular number mod n.

Original entry on oeis.org

1, 2, 2, 4, 2, 2, 2, 8, 2, 2, 2, 2, 4, 2, 2, 16, 5, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 32, 2, 5, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 64, 2, 2, 5, 5, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 4
Offset: 1

Views

Author

Ethan E. Wood, Jan 10 2025

Keywords

Comments

a(n) is the smallest nonnegative integer not in row n of A343713. - Pontus von Brömssen, Jan 11 2025

Examples

			For n=5, the triangular numbers mod 5 are the set {0,1,3} and the smallest number not in that set is a(5) = 2.

Crossrefs

Cf. A000079, A000217, A117484, A343713.

Programs

  • Maple
    f:= proc(n) local k;
     if n = 2^padic:-ordp(n,2) then return n fi;
     for k from 2 to n-1 do if NumberTheory:-QuadraticResidue(1+8*k,2*n)=-1 then return k fi od:
     FAIL
end proc:
map(f, [$1..200]); # Robert Israel, Jan 10 2025
  • PARI
    a(n)=setminus([1..n], Set(vector(n,k,k*(k-1)/2)%n))[1] \\ Andrew Howroyd, Jan 10 2025

A372810 a(n) is the smallest number whose Collatz trajectory contains n, if trajectories do not terminate at 1 but continue to cycle through 1, 4, 2, 1, 4, 2, 1, ... .

Original entry on oeis.org

1, 1, 3, 1, 3, 6, 7, 3, 9, 3, 7, 12, 7, 9, 15, 3, 7, 18, 19, 7, 21, 7, 15, 24, 25, 7, 27, 9, 19, 30, 27, 21, 33, 7, 15, 36, 37, 25, 39, 7, 27, 42, 43, 19, 45, 15, 27, 48, 43, 33, 51, 7, 15, 54, 55, 37, 57, 19, 39, 60, 27, 27, 63, 21, 43, 66, 39, 45, 69, 15, 27
Offset: 1

Views

Author

Ethan E. Wood, May 13 2024

Keywords

Comments

a(n) = A070167(n) for n >= 5.
a(n) = n if 3 divides n.

Examples

			For n=8,
  the trajectory of 1 is 1,  4, 2,  1, 4, ... (8 does not appear), and
  the trajectory of 2 is 2,  1, 4,  2, 1, ... (8 does not appear), but
  the trajectory of 3 is 3, 10, 5, 16, 8, ... (8 does appear),
so a(8) = 3.

References

  • R. K. Guy, Unsolved Problems in Number Theory, E16.

Links

Crossrefs

Cf. A070167 (sequence resulting if trajectories terminate at 1).

Extensions

Edited by Jon E. Schoenfield, May 13 2024

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