A047562 Numbers that are congruent to {3, 4, 5, 6, 7} mod 8.

3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 27, 28, 29, 30, 31, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 59, 60, 61, 62, 63, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 85, 86, 87, 91, 92, 93, 94, 95, 99, 100, 101, 102, 103

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From Chai Wah Wu, May 29 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.

G.f.: x*(x^5 + x^4 + x^3 + x^2 + x + 3)/(x^6 - x^5 - x + 1). (End)

From Wesley Ivan Hurt, Aug 16 2016: (Start)

a(n) = a(n-5) + 8 for n > 5.

a(n) = n + 2 + 3*floor((n-1)/5).

a(n) = (8*n + 7 - 3*((n+4) mod 5))/5.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-3, a(5k-3) = 8k-4, a(5k-4) = 8k-5. (End)

Maple

A047562:=n->8*floor(n/5)+[3, 4, 5, 6, 7][(n mod 5)+1]: seq(A047562(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2016

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {3, 4, 5, 6, 7, 11}, 50] (* G. C. Greubel, May 29 2016 *)
#+{3, 4, 5, 6, 7}&/@(8*Range[0, 20])//Flatten (* Harvey P. Dale, May 25 2020 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Aug 16 2016

Crossrefs

Sequence in context: A039056 A378086 A326754 * A354270 A137922 A176984

Adjacent sequences: A047559 A047560 A047561 * A047563 A047564 A047565

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved