A179850 Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.

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]

Links

Antti Karttunen, Table of n, a(n) for n = 0..4999

Michael Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

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

Cf. A003592, A047207, A011558, A130782.

Sequence in context: A085241 A105368 A138019 * A267919 A097343 A188011

Adjacent sequences: A179847 A179848 A179849 * A179851 A179852 A179853

Keyword

nonn

Author

Michael Somos, Jan 10 2011

Status

approved