A111958 Lucas numbers (A000032) mod 8.

2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7

Offset

0,1

Comments

This sequence has period-length 12.

Links

G. C. Greubel, Table of n, a(n) for n = 0..9999

Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1,-1,1,-1,1).

Formula

From G. C. Greubel, Feb 08 2016: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11).

a(n+12) = a(n). (End)

G.f.: (2 - x + 4*x^2 + 7*x^4 - 4*x^5 + 6*x^6 - x^7 + 8*x^8 - 4*x^9 + 7*x^10)/(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11). - Charles R Greathouse IV, May 16 2026

Mathematica

LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1}, {2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3}, 105] (* Ray Chandler, Aug 27 2015 *)
Mod[LucasL[Range[0, 99]], 8] (* Alonso del Arte, Dec 19 2015 *)

Prog

(PARI) a(n)=64016218314\8^(n%12)%8 \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A000032, A079344, A130893.

Sequence in context: A259773 A030133 A139374 * A192439 A160187 A257879

Adjacent sequences: A111955 A111956 A111957 * A111959 A111960 A111961

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2005

Status

approved