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A047588 Numbers that are congruent to {0, 1, 2, 3, 5, 6, 7} mod 8. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A165332 A171521 A092784 * A213257 A039213 A326947

Adjacent sequences:  A047585 A047586 A047587 * A047589 A047590 A047591

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 1 14:18 EDT 2020. Contains 333159 sequences. (Running on oeis4.)