OFFSET
1,1
COMMENTS
a(n) is the coefficient "a" in the Diophantine equation with two coefficients a and b, a * 2^n - b * 3^n = 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..2095
FORMULA
a(n) = ((3^n + 1)/2)^n mod 3^n (proved).
Conjecture: 2*a(n+1)-a(n) = 3^n * A055620(n). - Robert Israel, Mar 28 2017
EXAMPLE
2 * 2^1 mod 3^1 = 1, 7 * 2^2 mod 3^2 =1, 17 * 2^3 mod 3^3 = 1...
MAPLE
seq(2^(-n) mod 3^n, n=1..100); # Robert Israel, Mar 28 2017
MATHEMATICA
Table[ PowerMod[ (3^n +1)/2, n, 3^n], {n, 30}] (* Robert G. Wilson v, Mar 28 2017 *)
PROG
(PARI) a(n)= my(z=3^n); lift( Mod((z + 1)/2, z)^n); \\ Joerg Arndt, Mar 24 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Joe Slater, Mar 23 2017
EXTENSIONS
Corrected and more terms from Joerg Arndt, Mar 24 2017
STATUS
approved