A047595 Numbers that are congruent to {0, 1, 2, 3, 4, 5, 7} mod 8.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75

Offset

1,3

Comments

Complement of A017137. - Michel Marcus, Sep 15 2015

Links

Table of n, a(n) for n=1..67.

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

Formula

From Wesley Ivan Hurt, Sep 15 2015: (Start)

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

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

a(n) = n - 1 + floor(n/7). (End)

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

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

a(n) = (56*n - 70 - 6*(n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.

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

Maple

A047595:=n->n-1+floor(n/7): seq(A047595(n), n=1..100); # Wesley Ivan Hurt, Sep 15 2015

Mathematica

Table[n - 1 + Floor[n/7], {n, 100}] (* Wesley Ivan Hurt, Sep 15 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 7, 8}, 70] (* Vincenzo Librandi, Sep 16 2015 *)

Prog

(Magma) [n-1+Floor(n/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 15 2015
(Magma) I:=[0, 1, 2, 3, 4, 5, 7, 8]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..70]]; // Vincenzo Librandi, Sep 16 2015
(PARI) vector(200, n, n-1+floor(n/7)) \\ Altug Alkan, Oct 23 2015

Crossrefs

Cf. A017137 (8n+6).

Sequence in context: A183218 A071000 A088451 * A079298 A263715 A023055

Adjacent sequences: A047592 A047593 A047594 * A047596 A047597 A047598

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved