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

1,3

Comments

Complement of A017101. - Michel Marcus, Sep 13 2015

Links

Table of n, a(n) for n=1..72.

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

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)

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 *)

Prog

(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
(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

Crossrefs

Cf. A017101 (8n+3).

Sequence in context: A039212 A039221 A183297 * A039246 A201997 A358225

Adjacent sequences: A047570 A047571 A047572 * A047574 A047575 A047576

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Feb 19 2001

Status

approved