A079003 Least k >= 3 such that Fibonacci(k) == -1 (mod 3^n).

3, 6, 14, 38, 110, 326, 974, 2918, 8750, 26246, 78734, 236198, 708590, 2125766, 6377294, 19131878, 57395630, 172186886, 516560654, 1549681958, 4649045870, 13947137606, 41841412814, 125524238438, 376572715310, 1129718145926

Offset

1,1

References

R. L. Graham, D. E. Knuth and O. Patashnick, "Concrete Mathematics", second edition, Addison Wesley, ex. 6.59.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3).

Formula

a(1) = 3; for n > 1, a(n) = 3*a(n-1)-4; a(n) = 4*3^(n-2)+2.

From Colin Barker, May 01 2012: (Start)

a(n) = 4*a(n-1) - 3*a(n-2) for n > 3.

G.f.: x*(3 - 6*x - x^2)/((1-x)*(1-3*x)). (End)

E.g.f.: (1/9)*(4*exp(3*x) + 18*exp(x) - 3*x - 22). - Stefano Spezia, Nov 10 2019

Mathematica

CoefficientList[Series[(3-6*x-x^2)/((1-x)*(1-3*x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 23 2012 *)

Prog

(PARI) a(n)=if(n<0, 0, x=3; while((fibonacci(x)+1)%(3^n)>0, x++); x)
(Magma)  I:=[3, 6, 14, 38]; [n le 4 select I[n] else 4*Self(n-1) -3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012

Crossrefs

Sequence in context: A369544 A261436 A335580 * A099966 A101162 A274054

Adjacent sequences: A079000 A079001 A079002 * A079004 A079005 A079006

Keyword

nonn,easy

Author

Benoit Cloitre, Feb 01 2003

Status

approved