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A179850
Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.
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, 1, 1, 0, 1, 1
OFFSET
0,1
COMMENTS
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]
FORMULA
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, ...].
a(n) = A130782(n) mod 2. - Antti Karttunen, Aug 31 2017
EXAMPLE
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 + ...
MATHEMATICA
a[ n_] := Sign @ Mod[n - 2, 5]; (* Michael Somos, Jun 17 2015 *)
a[ n_] := {1, 0, 1, 1, 1}[[Mod[n, 5, 1]]]; (* Michael Somos, Jun 17 2015 *)
PROG
(PARI) {a(n) = sign( (n - 2) % 5 )};
(PARI) {a(n) = [1, 1, 0, 1, 1][n%5 + 1]};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 10 2011
STATUS
approved