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A229973
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Numbers coprime to 39.
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2
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1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22, 23, 25, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 53, 55, 56, 58, 59, 61, 62, 64, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 92, 94, 95, 97, 98, 100, 101, 103, 106
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OFFSET
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1,2
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COMMENTS
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Numbers not divisible by 3 or 13.
For n from 1 to 24, a(n) mod 39-n - floor(11*n/25)-2*floor(n/8) has a period of 24, consisting of all zeros except a -2 at indices 8, 16, and 24.
The asymptotic density of this sequence is 8/13. - Amiram Eldar, Oct 23 2020
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1).
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FORMULA
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a(n+24) = a(n) + 39.
a(n) = 39*floor((n-1)/24) + f(n) + floor(11*f(n)/25) + 2*floor(f(n)/8) - 2*floor(((n-1)mod 8)/7) + 40*floor(f(n-1)/23), where f(n) = n mod 24.
G.f.: x*(x^22+x^20+x^18+x^16+2*x^14-x^12+3*x^11-x^10+2*x^8+x^6+x^4+x^2+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)*(x^4+1)*(x^8-x^4+1)). - Colin Barker, Oct 07 2013
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MAPLE
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for n from 1 to 50 do if n mod 3<>0 and n mod 13<>0 then print(n) fi od
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MATHEMATICA
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CoefficientList[Series[(x^22 + x^20 + x^18 + x^16 + 2 x^14 - x^12 + 3 x^11 - x^10 + 2 x^8 + x^6 + x^4 + x^2 + 1)/((x - 1)^2 (x + 1) (x^2 - x + 1) (x^2 + 1) (x^4 - x^2 + 1) (x^4 + 1) (x^8 - x^4 + 1)), {x, 0, 80}], x] (* Vincenzo Librandi, Oct 08 2013 *)
Select[Range[100], CoprimeQ[39, #] &] (* Amiram Eldar, Oct 23 2020 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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