A004774 Numbers n whose binary expansion does not end in 001.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77

Offset

1,3

Comments

Numbers less than 8 or not congruent to 1 (mod 8). - M. F. Hasler, Nov 02 2013

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

From Colin Barker, Jul 23 2016: (Start)

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

G.f.: x^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^8) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)).

(End)

a(1) = 0, a(2) = 1, a(7*n + k + 2) = 8*n + k + 1, n >= 0, 1 <= k < 8. - Yosu Yurramendi, Aug 09 2016

Mathematica

Join[Range[0, 3], Select[Range[4, 80], Take[IntegerDigits[#, 2], -3] != {0, 0, 1} &]]  (* Harvey P. Dale, Feb 18 2011 *)
Table[If[n < 9, n - 1, Floor[(8 n - 10)/7]], {n, 69}] (* or *)
Rest@ CoefficientList[Series[x^2 (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^8)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 69}], x] (* Michael De Vlieger, Aug 10 2016 *)

Prog

(PARI) a(n)=if(n<9, n-1, (8*n-10)\7) \\ Charles R Greathouse IV, Mar 26 2013
(PARI) concat(0, Vec(x^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^8)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^100))) \\ Colin Barker, Jul 23 2016

Crossrefs

Sequence in context: A032856 A023751 A047594 * A191845 A274375 A364542

Adjacent sequences: A004771 A004772 A004773 * A004775 A004776 A004777

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved