A082511 a(n) = 3^n mod 2n.

1, 1, 3, 1, 3, 9, 3, 1, 9, 9, 3, 9, 3, 9, 27, 1, 3, 9, 3, 1, 27, 9, 3, 33, 43, 9, 27, 25, 3, 9, 3, 1, 27, 9, 47, 9, 3, 9, 27, 1, 3, 57, 3, 81, 63, 9, 3, 33, 31, 49, 27, 81, 3, 81, 67, 65, 27, 9, 3, 81, 3, 9, 27, 1, 113, 69, 3, 81, 27, 109, 3, 81, 3, 9, 57, 81, 75, 105, 3, 1, 81, 9, 3, 57, 73

Offset: 1

Author

Labos Elemer, Apr 28 2003

Keywords

• nonn

Examples

			Residues are often also powers of 3, that is, 3^n = k*2*n + 3^j, as is the case for n=1..23. The first terms that are not powers of 3 are a(24)=33 and a(25)=43.
a(6)=9: modulus = 2*n = 12; 3^n = 3^6 = 729 = 60*12 + 9 = 720 + a(6).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000079, A000244, A002379.

Cf. A083528, A083529, A083530.

Programs

Mathematica

Table[PowerMod[3,n,2n],{n,90}] (* Harvey P. Dale, Jan 21 2014 *)

PARI

a(n) = lift(Mod(3, 2*n)^n) \\ Felix Fröhlich, Oct 20 2018

Python

for n in range(1, 80): print(pow(3, n, 2*n), end=" ") # Stefano Spezia, Oct 20 2018