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A004774 Numbers n whose binary expansion does not end in 001. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Numbers less than 8 or not congruent to 1 (mod 8). - M. F. Hasler, Nov 02 2013
LINKS
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 21 16:35 EDT 2024. Contains 371874 sequences. (Running on oeis4.)