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
Keywords
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.
Programs
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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
Comments