A004776 Numbers not congruent to 5 (mod 8).

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78

Offset

1,3

Comments

Also, numbers whose binary expansion does not end in 101.

Numbers that are congruent to {0, 1, 2, 3, 4, 6, 7} mod 8. - 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

Numbers that are congruent to {0, 1, 2, 3, 4, 6, 7} mod 8.

G.f.: x^2*(1+x+x^2+x^3+2*x^4+x^5+x^6) / ((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2). - R. J. Mathar, Oct 25 2011

a(n) = n + floor((n-6)/7). - M. F. Hasler, Nov 02 2013

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

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

a(n) = (56*n - 63 + (n mod 7) - 6*((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.

a(7k) = 8k-1, a(7k-1) = 8k-2, a(7k-2) = 8k-4, a(7k-3) = 8k-5, a(7k-4) = 8k-6, a(7k-5) = 8k-7, a(7k-6) = 8k-8. (End)

Maple

A004776:=n->8*floor(n/7)+[0, 1, 2, 3, 4, 6, 7][(n mod 7)+1]: seq(A004776(n), n=0..100); # Wesley Ivan Hurt, Jul 22 2016

Mathematica

DeleteCases[Range[0, 80], _?(Mod[#, 8]==5&)] (* Harvey P. Dale, Apr 28 2014 *)

Prog

(Haskell)
a004776 n = a004776_list !! (n-1)
a004776_list = filter ((/= 5) . (`mod` 8)) [0..]
-- Reinhard Zumkeller, Aug 17 2012
(PARI) is(n)=n%8!=5 \\ Charles R Greathouse IV, Mar 07 2013
(PARI) A004776(n)=n+(n-6)\7  \\ M. F. Hasler, Nov 02 2013
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 4, 6, 7]]; // Wesley Ivan Hurt, Jul 22 2016
(Python)
def A004776(n): return n-1+(n+1)//7 # Chai Wah Wu, Feb 24 2025

Crossrefs

Cf. A004770 (complement), A045323 (primes).

Sequence in context: A101771 A035058 A350757 * A187945 A137409 A037041

Adjacent sequences: A004773 A004774 A004775 * A004777 A004778 A004779

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Nov 02 2013

Status

approved