A004777 Numbers not congruent to 7 mod 8.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers that are congruent to {0, 1, 2, 3, 4, 5, 6} mod 8.

Numbers n such that binary expansion does not end 111.

Complement of A004771. - Michel Marcus, Sep 11 2015

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Crossrefs

Cf. A004771, A059561, A132270.

Programs

Magma

[n-1+Floor((n-1)/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 11 2015

Magma

[n: n in [0..100] | not n mod 8 in [7]]; // Vincenzo Librandi, Sep 11 2015

Maple

A004777:=n->n-1+floor((n-1)/7): seq(A004777(n), n=1..100); # Wesley Ivan Hurt, Sep 11 2015

Mathematica

DeleteCases[Range[0,100],?(Mod[#,8]==7&)] (* _Harvey P. Dale, Apr 01 2011 *)
Select[Range[0, 100], ! MemberQ[{7}, Mod[#, 8]] &] (* Vincenzo Librandi, Sep 12 2015 *)

PARI

A004777=n->(n-1)*8\7 \\ M. F. Hasler, Nov 02 2013

Formula

G.f.: x^2*(1+x+x^2+x^3+x^4+x^5+2*x^6) / ((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = floor((n-1)*8/7). - M. F. Hasler, Nov 02 2013

From Wesley Ivan Hurt, Sep 11 2015: (Start)

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

a(n) = n - 1 + A132270(n). (End)

From Wesley Ivan Hurt, Jul 20 2016: (Start)

a(n) = (56*n - 77 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) - 6*((n+6) mod 7))/49.

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

Extensions

Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of R. J. Mathar.