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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A017137. - Michel Marcus, Sep 15 2015

Links

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

Crossrefs

Cf. A017137 (8n+6).

Programs

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

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 *)

PARI

vector(200, n, n-1+floor(n/7)) \\ Altug Alkan, Oct 23 2015

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)