A079004 Least x>=3 such that F(x)==1 (mod 3^n) where F(x) denotes the x-th Fibonacci number (A000045).

7, 10, 10, 34, 106, 322, 970, 2914, 8746, 26242, 78730, 236194, 708586, 2125762, 6377290, 19131874, 57395626, 172186882, 516560650, 1549681954, 4649045866, 13947137602, 41841412810, 125524238434, 376572715306, 1129718145922

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..26.

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

Formula

a(1)=7, a(2)=10, a(3)=10; for n>3, a(n) = 3*a(n-1) + 4.

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

G.f.: 8*x^2+(23/3)*x+14/9+2/(x-1)-4/(9*(3*x-1)). - Robert Israel, Jan 15 2015

Maple

7, 10, seq(4*3^(n-2)-2, n=3..50); # Robert Israel, Jan 15 2015

Mathematica

a=2; lst={7, 10}; Do[a=a*3+4; AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)
LinearRecurrence[{4, -3}, {7, 10, 10, 34}, 40] (* Harvey P. Dale, Aug 16 2024 *)

Prog

(PARI) a(n)=if(n<0, 0, x=3; while((fibonacci(x)-1)%(3^n)>0, x++); x)

Crossrefs

Cf. A000045, A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, A100774.

Sequence in context: A225694 A247191 A317336 * A265311 A192268 A117319

Adjacent sequences: A079001 A079002 A079003 * A079005 A079006 A079007

Keyword

nonn,easy

Author

Benoit Cloitre, Feb 01 2003

Extensions

Formula corrected by Robert Israel, Jan 15 2015

Status

approved