A047586 Numbers that are congruent to {2, 3, 5, 6, 7} mod 8.

2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 18, 19, 21, 22, 23, 26, 27, 29, 30, 31, 34, 35, 37, 38, 39, 42, 43, 45, 46, 47, 50, 51, 53, 54, 55, 58, 59, 61, 62, 63, 66, 67, 69, 70, 71, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 90, 91, 93, 94, 95, 98, 99, 101, 102, 103

Offset

1,1

Links

Table of n, a(n) for n=1..65.

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

Formula

From Wesley Ivan Hurt, Jul 28 2016: (Start)

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

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 5 + 3*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) - 7*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-3, a(5k-3) = 8k-5, a(5k-4) = 8k-6. (End)

Maple

A047586:=n->8*floor(n/5)+[(2, 3, 5, 6, 7)][(n mod 5)+1]: seq(A047586(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Select[Range[0, 300], MemberQ[{2, 3, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 28 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {2, 3, 5, 6, 7, 10}, 80] (* Harvey P. Dale, Aug 10 2023 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jul 28 2016

Crossrefs

Sequence in context: A077337 A093501 A087007 * A103841 A003754 A293427

Adjacent sequences: A047583 A047584 A047585 * A047587 A047588 A047589

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved