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

1,3

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A004771, A059561, A132270.

Sequence in context: A257458 A179439 A047421 * A059561 A037474 A292638

Adjacent sequences: A004774 A004775 A004776 * A004778 A004779 A004780

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved