A047603 Numbers that are congruent to {1, 2, 3, 4, 5} mod 8.

1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 17, 18, 19, 20, 21, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 41, 42, 43, 44, 45, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 81, 82, 83, 84, 85, 89, 90, 91, 92, 93, 97, 98, 99, 100, 101

Offset

1,2

Links

Vincenzo Librandi, 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, Jun 10 2016: (Start)

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

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

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

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

a(n) = (40*n - 45 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 12*((n+4) mod 5))/25.

a(5k) = 8k-3, a(5k-1) = 8k-4, a(5k-2) = 8k-5, a(5k-3) = 8k-6, a(5k-4) = 8k-7. (End)

a(n) = n + 3*floor((n-1)/5). - Wesley Ivan Hurt, Aug 08 2016

Maple

A047603:=n->8*floor(n/5)+[(1, 2, 3, 4, 5)][(n mod 5)+1]: seq(A047603(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 28 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 9}, 100] (* Vincenzo Librandi, Aug 08 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1..5]]; // Wesley Ivan Hurt, Jul 28 2016

Crossrefs

Sequence in context: A119955 A158573 A194398 * A047362 A032969 A095906

Adjacent sequences: A047600 A047601 A047602 * A047604 A047605 A047606

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved