A047588 Numbers that are congruent to {0, 1, 2, 3, 5, 6, 7} mod 8.

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81

Offset

1,3

Links

Table of n, a(n) for n=1..72.

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Formula

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

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

From Wesley Ivan Hurt, Jul 21 2016: (Start)

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

a(n) = (56*n - 56 + (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.

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

Maple

A047588:=n->8*floor(n/7)+[0, 1, 2, 3, 5, 6, 7][(n mod 7)+1]: seq(A047588(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016

Mathematica

Complement[Range[100], 4Range[1, 99, 2]] (* Harvey P. Dale, Jan 29 2011 *)

Prog

(PARI) a(n)=n+1+(n-4)\7
(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jul 21 2016

Crossrefs

Sequence in context: A171521 A352796 A092784 * A213257 A367401 A039213

Adjacent sequences: A047585 A047586 A047587 * A047589 A047590 A047591

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved