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A057427 Sign(n) or signum(n) (with offset 0): a(n) = 1 if n>0, = 0 if n=0, = -1 if n<0; series expansion of x/(1-x). 112
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Parity of (n+1)-st prime, A000040(n+1). - Philippe Deléham, Apr 04 2009

Decimal expansion of 1/90.

Partial sums of A063524 (characteristic function of 1). - Jeremy Gardiner, Sep 08 2002

Characteristic function of positive integers. - Franklin T. Adams-Watters, Aug 01 2011

Number of binary bracelets of n beads, 0 of them 0. Number of binary bracelets of n beads, 1 of them 0. Number of binary bracelets of n beads, 0 of them 0, with 00 prohibited. For n>=2, a(n-1) is the number of binary bracelets of n beads, one of them 0, with 00 prohibited. - Washington Bomfim, Aug 27 2008

a(A000027(n)) = 1; a(A000004(n)) = 0. - Reinhard Zumkeller, Oct 11 2008

Central terms of the triangle in A152487. - Reinhard Zumkeller, Dec 06 2008

See sequence A261012 for a version that extends the sequence backwards to offset -1.

REFERENCES

T. M. MacRobert, Functions of a Complex Variable, 4th ed., Macmillan and Co., London, 1958, p. 90.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for characteristic functions

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

FORMULA

G.f.: x / (1 - x).

G.f.: Sum_{k>=0} 2^k * x^(2^k) / (1 + x^(2^k)). - Michael Somos, Sep 11 2005

a(n) = A000007(0^n). - Jaume Oliver Lafont, Mar 19 2009

a(n) = - a(-n) for all n in Z. - Michael Somos, Aug 17 2015

Sum{k<0} a(k) * x^k = 1 / (1 - x) if abs(x) > 1. - Michael Somos, Aug 17 2015

Dirichlet g.f.: zeta(s). - Álvar Ibeas, Nov 29 2015

EXAMPLE

1/90 = .0111111111111111111...

G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + ...

MAPLE

with(numtheory); A057427:=n->signum(n); seq(A057427(k), k=0..50); # Wesley Ivan Hurt, Oct 22 2013

MATHEMATICA

Table[Sign[n], {n, 0, 104}] (* Arkadiusz Wesolowski, Sep 16 2012 *)

CoefficientList[Series[x/((1 - x)), {x, 0, 25}], x]

LinearRecurrence[{1, 0}, {0, 1}, 105]

Array[Sign, 105, 0]

N[1/9, 111]

PROG

(PARI) {a(n) = sign(n)};

(PARI) /* n>=0 */ a(n)=!!n \\ Jaume Oliver Lafont, Mar 19 2009

(Haskell)

a057427 = signum

a057427_list = 0 : [1, 1 ..]  -- Reinhard Zumkeller, Nov 28 2012

CROSSREFS

Cf. A000004, A000007, A000012, A000027, A000040, A063524, A152487.

See also A261012.

Sequence in context: A103131 A112347 * A178334 A185016 A185015 A185014

Adjacent sequences:  A057424 A057425 A057426 * A057428 A057429 A057430

KEYWORD

nonn,easy,mult,nice,cons

AUTHOR

Henry Bottomley, Sep 05 2000

EXTENSIONS

Entry edited at the suggestion of Robert G. Wilson v by N. J. A. Sloane, Aug 16 2015

STATUS

approved

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Last modified May 28 10:09 EDT 2017. Contains 287240 sequences.