A047592 Numbers that are congruent to {1, 2, 3, 4, 5, 6, 7} mod 8.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81

Offset

1,2

Comments

Or, numbers that are not multiples of 8. - Benoit Cloitre, Jul 11 2009

More generally the sequence of numbers not divisible by some fixed integer m >= 2 is given by a(n, m) = n - 1 + floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009

Complement of A008590. - Reinhard Zumkeller, Nov 30 2009

Links

Vincenzo Librandi, 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).

Formula

a(n) = n - 1 + floor((n+6)/7). - Benoit Cloitre, Jul 11 2009

A168181(a(n)) = 1. - Reinhard Zumkeller, Nov 30 2009

From R. J. Mathar, Mar 08 2011: (Start)

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

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

a(n) = A207481(n) for n <= 70. - Reinhard Zumkeller, Feb 18 2012

From Wesley Ivan Hurt, Jul 20 2016: (Start)

a(n) = (56*n - 28 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) - 6*((n+6) mod 7))/49.

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

Sum_{n>=1} (-1)^(n+1)/a(n) = (4*sqrt(sqrt(2)+2) - 2*sqrt(2) - 1)*Pi/16. - Amiram Eldar, Dec 28 2021

Maple

A047592:=n->8*floor(n/7)+[1, 2, 3, 4, 5, 6, 7][(n mod 7)+1]: seq(A047592(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016

Mathematica

Complement[Range[88], 8Range[11]] (* Harvey P. Dale, Jan 22 2011 *)
CoefficientList[Series[(1 + x)*(1 + x^2)*(1 + x^4)/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Jan 06 2013 *)

Prog

(PARI) a(n)=n-1+floor((n+6)/7) \\ Benoit Cloitre, Jul 11 2009
(Magma) [ n: n in [0..100] | n mod 8 in {1, 2, 3, 4, 5, 6, 7} ]; // Vincenzo Librandi, Dec 25 2010]

Crossrefs

Cf. A008590, A168181, A207481.

Sequence in context: A182768 A368917 A207481 * A187320 A255805 A043093

Adjacent sequences: A047589 A047590 A047591 * A047593 A047594 A047595

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved