A079004 - OEIS

%I #22 Aug 16 2024 12:37:59

%S 7,10,10,34,106,322,970,2914,8746,26242,78730,236194,708586,2125762,

%T 6377290,19131874,57395626,172186882,516560650,1549681954,4649045866,

%U 13947137602,41841412810,125524238434,376572715306,1129718145922

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

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

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

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

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

%p 7, 10, seq(4*3^(n-2)-2,n=3..50); # _Robert Israel_, Jan 15 2015

%t a=2;lst={7,10};Do[a=a*3+4;AppendTo[lst,a],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008 *)

%t LinearRecurrence[{4,-3},{7,10,10,34},40] (* _Harvey P. Dale_, Aug 16 2024 *)

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

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

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Feb 01 2003

%E Formula corrected by _Robert Israel_, Jan 15 2015