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

Author

Benoit Cloitre, Feb 01 2003

Keywords

• nonn
• easy

References

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

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

Extensions

Formula corrected by Robert Israel, Jan 15 2015