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A047592
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Numbers that are congruent to {1, 2, 3, 4, 5, 6, 7} mod 8.
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8
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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]
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CROSSREFS
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Cf. A008590, A168181, A207481.
Sequence in context: A329135 A182768 A207481 * A187320 A255805 A043093
Adjacent sequences: A047589 A047590 A047591 * A047593 A047594 A047595
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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