A047573 Numbers that are congruent to {0, 1, 2, 4, 5, 6, 7} mod 8.

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A017101. - Michel Marcus, Sep 13 2015

Links

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

Crossrefs

Cf. A017101 (8n+3).

Programs

Magma

[n+Floor((n-4)/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 12 2015

Magma

I:=[0,1,2,4,5,6,7,8]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..80]]; // Vincenzo Librandi, Sep 13 2015

Maple

for n from 0 to 200 do if n mod 8 <> 3 then printf(`%d,`,n) fi: od:

Mathematica

Table[n+Floor[(n-4)/7], {n, 100}] (* Wesley Ivan Hurt, Sep 12 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7, 8}, 80] (* Vincenzo Librandi, Sep 13 2015 *)
DeleteCases[Range[0,100],?(Mod[#,8]==3&)] (* _Harvey P. Dale, Oct 05 2020 *)

Python

def A047573(n):
    a, b = divmod(n-1,7)
    return (0,1,2,4,5,6,7)[b]+(a<<3) # Chai Wah Wu, Jan 27 2023

Formula

G.f.: x^2*(x^6+x^5+x^4+x^3+2*x^2+x+1)/((x-1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)). [Colin Barker, Jun 22 2012]

From Wesley Ivan Hurt, Sep 12 2015: (Start)

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

a(n) = n + floor((n-4)/7). (End)

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

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

a(n) = (56*n - 49 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) - 6*((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-2, a(7*k-2) = 8*k-3, a(7*k-3) = 8*k-4, a(7*k-4) = 8*k-6, a(7*k-5) = 8*k-7, a(7*k-6) = 8*k-8. (End)

Extensions

More terms from James Sellers, Feb 19 2001