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A079004 Least x>=3 such that F(x)==1 (mod 3^n) where F(x) denotes the x-th Fibonacci number (A000045). 4
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified September 21 22:32 EDT 2020. Contains 337274 sequences. (Running on oeis4.)