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A047443 Numbers that are congruent to {3, 5, 6} mod 8. 3
3, 5, 6, 11, 13, 14, 19, 21, 22, 27, 29, 30, 35, 37, 38, 43, 45, 46, 51, 53, 54, 59, 61, 62, 67, 69, 70, 75, 77, 78, 83, 85, 86, 91, 93, 94, 99, 101, 102, 107, 109, 110, 115, 117, 118, 123, 125, 126, 131, 133, 134, 139, 141, 142, 147, 149, 150, 155, 157, 158 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, numbers n such that Fibonacci(n) = 2 (mod 3), where Fibonacci = A000045. - M. F. Hasler, Sep 29 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

G.f.: x*(1+x)*(2*x^2-x+3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 2*(12*n-3-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-3, a(3k-2) = 8k-5. (End)

MAPLE

A047443:=n->2*(12*n-3-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9: seq(A047443(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

MATHEMATICA

Select[Range[150], MemberQ[{3, 5, 6}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2011 *)

LinearRecurrence[{1, 0, 1, -1}, {3, 5, 6, 11}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(PARI) is_A047443(n)=bittest(104, n%8) \\ with 104=2^3+2^5+2^6. - M. F. Hasler, Sep 29 2012

(PARI) A047443(n)={n=divrem(n, 3); n[1]*8+[-2, 3, 5][n[2]+1]} \\ M. F. Hasler, Sep 29 2012

(MAGMA) [n : n in [0..150] | n mod 8 in [3, 5, 6]]; // Wesley Ivan Hurt, Jun 13 2016

CROSSREFS

Cf. A000045.

Sequence in context: A285785 A080759 A145714 * A173593 A268495 A127577

Adjacent sequences:  A047440 A047441 A047442 * A047444 A047445 A047446

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 21 08:53 EDT 2019. Contains 323441 sequences. (Running on oeis4.)