

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.


2



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
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OFFSET

0,1


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.


LINKS

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


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.


EXAMPLE

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


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 *)


PROG

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


CROSSREFS

Cf. A239130.
Sequence in context: A031136 A050456 A107930 * A033400 A306414 A207144
Adjacent sequences: A239128 A239129 A239130 * A239132 A239133 A239134


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Mar 22 2014


EXTENSIONS

More terms from Vincenzo Librandi, Mar 23 2014


STATUS

approved



