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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 (list; graph; refs; listen; history; text; internal format)
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

M. 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, ...].

25*a(n) = 2*(n mod 5)+2*[(n+1) mod 5]-3*[(n+2) mod 5]+7*[(n+3) mod 5]+2*[(n+4) mod 5] - Paolo P. Lava, Mar 10 2011

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

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Last modified November 12 07:03 EST 2019. Contains 329052 sequences. (Running on oeis4.)