

A082511


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


4



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
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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 FrÃ¶hlich, Oct 20 2018


CROSSREFS

Cf. A000079, A000244, A002379.
Cf. A083528, A083529, A083530.
Sequence in context: A143453 A248830 A164308 * A265307 A133579 A088442
Adjacent sequences: A082508 A082509 A082510 * A082512 A082513 A082514


KEYWORD

nonn


AUTHOR

Labos Elemer, Apr 28 2003


STATUS

approved



