A047594 Numbers that are congruent to {0, 2, 3, 4, 5, 6, 7} mod 8.

0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76

Offset

1,2

Comments

A004774 without the 1. - R. J. Mathar, Oct 18 2008

Complement of A017077. - Michel Marcus, Sep 11 2015

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Formula

From R. J. Mathar, Mar 03 2009: (Start)

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

a(n) = a(n-7) + 8 for n>7. (End)

a(n) = n + floor((n-2)/7). - Wesley Ivan Hurt, Sep 11 2015

From Wesley Ivan Hurt, Jul 21 2016: (Start)

a(n) = a(n-1) + a(n-7) - a(n-8) for n>8.

a(n) = (56*n - 35 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) - 6*((n+5) mod 7) + ((n+6) mod 7))/49.

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

Maple

A047594:=n->n+floor((n-2)/7): seq(A047594(n), n=1..100); # Wesley Ivan Hurt, Sep 11 2015

Mathematica

Table[n+Floor[(n-2)/7], {n, 100}] (* Wesley Ivan Hurt, Sep 11 2015 *)
Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, Sep 12 2015 *)
DeleteCases[Range[0, 70], _?(Mod[#, 8]==1&)] (* Harvey P. Dale, Dec 19 2015 *)

Prog

(Magma) [n + Floor((n-2)/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 11 2015
(Magma) [n: n in [0..100] | n mod 8 in [0, 2, 3, 4, 5, 6, 7]]; // Vincenzo Librandi, Sep 12 2015
(PARI) a(n)=(8*n-2)\7 \\ Charles R Greathouse IV, Jul 21 2016

Crossrefs

Cf. A004774, A017077.

Sequence in context: A032897 A032856 A023751 * A004774 A191845 A274375

Adjacent sequences: A047591 A047592 A047593 * A047595 A047596 A047597

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved