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

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

1,2

Comments

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

Links

Table of n, a(n) for n=1..94.

Example

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.

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

Prog

(PARI) a(n)=setminus([1..n], Set(vector(n, k, k*(k-1)/2)%n))[1] \\ Andrew Howroyd, Jan 10 2025

Crossrefs

Cf. A000079, A000217, A117484, A343713.

Sequence in context: A215847 A360460 A057000 * A348044 A328400 A239676

Adjacent sequences: A380033 A380034 A380035 * A380037 A380038 A380039

Keyword

nonn,new

Author

Ethan E. Wood, Jan 10 2025

Status

approved