A047594 Numbers that are congruent to {0, 2, 3, 4, 5, 6, 7} mod 8.
0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
Programs
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Magma
[n + Floor((n-2)/7) : n in [1..100]]; // Wesley Ivan Hurt, Sep 11 2015
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Magma
[n: n in [0..100] | n mod 8 in [0,2,3,4,5,6,7]]; // Vincenzo Librandi, Sep 12 2015
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Maple
A047594:=n->n+floor((n-2)/7): seq(A047594(n), n=1..100); # Wesley Ivan Hurt, Sep 11 2015
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Mathematica
Table[n+Floor[(n-2)/7], {n,100}] (* Wesley Ivan Hurt, Sep 11 2015 *) Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, Sep 12 2015 *) DeleteCases[Range[0,70],?(Mod[#,8]==1&)] (* _Harvey P. Dale, Dec 19 2015 *) -
PARI
a(n)=(8*n-2)\7 \\ Charles R Greathouse IV, Jul 21 2016
Formula
From R. J. Mathar, Mar 03 2009: (Start)
G.f.: x^2*(2+x+x^2+x^3+x^4+x^5+x^6)/((1-x)^2*(x^6+x^5+x^4+x^3+x^2+x+1)).
a(n) = a(n-7) + 8 for n>7. (End)
a(n) = n + floor((n-2)/7). - Wesley Ivan Hurt, Sep 11 2015
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 - 35 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) - 6*((n+5) mod 7) + ((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-8. (End)
Comments