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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

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 *)

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

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