A239131 A sequence with period length 54; the companion of x(n) = A239130(n), the smallest positive solution of 3^4*x - 2^n*y = 1 for n >= 0.

80, 40, 20, 10, 5, 43, 62, 31, 56, 28, 14, 7, 44, 22, 11, 46, 23, 52, 26, 13, 47, 64, 32, 16, 8, 4, 2, 1, 41, 61, 71, 76, 38, 19, 50, 25, 53, 67, 74, 37, 59, 70, 35, 58, 29, 55, 68, 34, 17, 49, 65, 73, 77, 79, 80, 40, 20, 10, 5, 43, 62, 31, 56, 28, 14, 7, 44

Offset: 0

Author

Wolfdieter Lang, Mar 22 2014

Keywords

• nonn
• easy

Comments

The first 54 = phi(3^4) values of a(n) = y0(4, n) have been given, with phi(n) = A000010(n). They give a permutation of the smallest positive restricted residue class modulo 3^4.

The companion sequence is x0(4, n) = x(n) = A239130(n), n >= 0.

One could give a lengthy G.f.

Examples

			a(0) = 41^27 (mod 81) = 80.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A239130.

Programs

Magma

[41^(n+27) mod 81: n in [0..80]]; // Vincenzo Librandi, Mar 23 2014

Mathematica

Table[Mod[41^(n + 27), 81], {n, 0, 100}] (* Vincenzo Librandi, Mar 23 2014 *)
PowerMod[41,Range[0,100]+27,81] (* Harvey P. Dale, Dec 04 2018 *)

Formula

a(n) = y0(4, n) == ((3^4 + 1)/2)^(n + 3^3) (mod 3^4), n >= 0.

a(n + 54) = a(n), n >= 0.

Extensions

More terms from Vincenzo Librandi, Mar 23 2014