A004775 Numbers k such that the binary expansion of k does not end in 011.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 76, 77

Offset

1,3

Comments

Numbers less than 8 or not congruent to 3 (mod 8). - M. F. Hasler, Nov 02 2013

Numbers that are congruent to {0, 1, 2, 4, 5, 6, 7} mod 8 including the number "3". - Wesley Ivan Hurt, Jul 22 2016

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

For all n>4, a(n) = n + floor((n-12)/7); for n<12, a(n) = n-1. - M. F. Hasler, Nov 02 2013

From Wesley Ivan Hurt, Jul 22 2016: (Start)

G.f.: x^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^10)/(1 - x - x^7 + x^8).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>12; a(n) = a(n-7) + 8 for n>11.

a(n) = (56*n - 105 + (n mod 7) + ((n+1) mod 7) - 6*((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49 for n>4. (End)

a(1) = 0, a(2) = 1, a(3) = 2, a(4) = 3, a(7*n + k + 4) = 8*n + k + 3, n >= 0, 1 <= k < 8. - Yosu Yurramendi, Aug 09 2016

Example

9 is 1001 in binary, which ends 001, not 011, so 9 is in the sequence.  19 is 10011 in binary, which ends 011, so 19 is not in the sequence. - Michael B. Porter, Jul 22 2016

Maple

A004775:=n->8*floor(n/7)+[0, 1, 2, 4, 5, 6, 7][(n mod 7)+1]: 0, 1, 2, 3, seq(A004775(n), n=3..100); # Wesley Ivan Hurt, Jul 22 2016

Mathematica

Join[{0, 1, 2, 3}, Select[Range[3, 150], MemberQ[{0, 1, 2, 4, 5, 6, 7}, Mod[#, 8]] &]] (* Wesley Ivan Hurt, Jul 22 2016 *)

Prog

(PARI) is(n)=n%8!=3 || n==3 \\ Charles R Greathouse IV, Mar 29 2013
(PARI) A004775(n)=n+(n-5)\7-(n>4) \\  M. F. Hasler, Nov 02 2013
(Magma) [0..3] cat [n : n in [3..100] | n mod 8 in [0, 1, 2, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jul 22 2016

Crossrefs

Sequence in context: A333501 A369092 A247801 * A231238 A231239 A335523

Adjacent sequences: A004772 A004773 A004774 * A004776 A004777 A004778

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved