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

1,3

Links

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

Example

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).

Mathematica

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

Prog

(Python) for n in range(1, 80): print(pow(3, n, 2*n), end=" ") # Stefano Spezia, Oct 20 2018
(PARI) a(n) = lift(Mod(3, 2*n)^n) \\ Felix Fröhlich, Oct 20 2018

Crossrefs

Cf. A000079, A000244, A002379.

Cf. A083528, A083529, A083530.

Sequence in context: A248830 A350562 A164308 * A265307 A133579 A088442

Adjacent sequences: A082508 A082509 A082510 * A082512 A082513 A082514

Keyword

nonn

Author

Labos Elemer, Apr 28 2003

Status

approved