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A004775 Numbers k such that the binary expansion of k does not end in 011. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A247806 A333501 A247801 * A231238 A231239 A328869

Adjacent sequences:  A004772 A004773 A004774 * A004776 A004777 A004778

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)