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A179850
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Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.
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1
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1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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a(n) is also the characteristic sequence for the mod m reduced odd numbers (i.e., gcd(2*n+1,m)=1, n>=0) for each modulus m from 5*A003592 = [5, 10, 20, 25, 40, 50, 80, 100, 125,...]. [Wolfdieter Lang, Feb 04 2012]
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LINKS
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FORMULA
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a(n) = b(2*n + 1) where b(n) is completely multiplicative with b(2) = b(5) = 0, otherwise b(p) = 1.
Coefficient of q^(2*n + 1) in q * (1 - q^4) * (1 - q^12) / ((1 - q^2) * (1 - q^6) * (1 - q^10)).
Euler transform of length 6 sequence [1, -1, 1, 0, 1, -1].
G.f.: (1 + x) * (1 + x^3) / (1 - x^5).
a(n) = a(-n) = a(n + 5) = A011558(n + 3) for all n in Z.
Period 5 sequence [1, 1, 0, 1, 1, ...].
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EXAMPLE
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G.f. = 1 + x + x^3 + x^4 + x^5 + x^6 + x^8 + x^9 + x^10 + x^11 + x^13 + ...
G.f. = q + q^3 + q^7 + q^9 + q^11 + q^13 + q^17 + q^19 + q^21 + q^23 + ...
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MATHEMATICA
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a[ n_] := {1, 0, 1, 1, 1}[[Mod[n, 5, 1]]]; (* Michael Somos, Jun 17 2015 *)
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PROG
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(PARI) {a(n) = sign( (n - 2) % 5 )};
(PARI) {a(n) = [1, 1, 0, 1, 1][n%5 + 1]};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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