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A047595 Numbers that are congruent to {0, 1, 2, 3, 4, 5, 7} mod 8. 2
0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Complement of A017137. - Michel Marcus, Sep 15 2015

LINKS

Table of n, a(n) for n=1..67.

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

FORMULA

From Wesley Ivan Hurt, Sep 15 2015: (Start)

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

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

a(n) = n - 1 + floor(n/7). (End)

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

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

a(n) = (56*n - 70 - 6*(n mod 7) + ((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(7*k) = 8*k-1, a(7*k-1) = 8*k-3, a(7*k-2) = 8*k-4, 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

A047595:=n->n-1+floor(n/7): seq(A047595(n), n=1..100); # Wesley Ivan Hurt, Sep 15 2015

MATHEMATICA

Table[n - 1 + Floor[n/7], {n, 100}] (* Wesley Ivan Hurt, Sep 15 2015 *)

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 7, 8}, 70] (* Vincenzo Librandi, Sep 16 2015 *)

PROG

(MAGMA) [n-1+Floor(n/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 15 2015

(MAGMA) I:=[0, 1, 2, 3, 4, 5, 7, 8]; [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..70]]; // Vincenzo Librandi, Sep 16 2015

(PARI) vector(200, n, n-1+floor(n/7)) \\ Altug Alkan, Oct 23 2015

CROSSREFS

Cf. A017137 (8n+6).

Sequence in context: A183218 A071000 A088451 * A079298 A263715 A023055

Adjacent sequences:  A047592 A047593 A047594 * A047596 A047597 A047598

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 18 20:25 EST 2019. Contains 320262 sequences. (Running on oeis4.)