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
Central terms of the triangle in A152487. - Reinhard Zumkeller, Dec 06 2008
This is sgn(n) (or sign(n), or signum(n)) restricted to nonnegative integers. 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
Elizabeth Hartung, Brett Stevens, and Aaron Williams, Pyramid Schemes for Eating M&Ms: Enumeration, Generation, and Gray Codes, LIPIcs Vol. 366, 13th Int'l Conf. Fun Algor. (FUN 2026), Art. 23. See p. 20 (Table 5).
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
From Michael Somos, Aug 17 2015: (Start)
a(n) = -a(-n) for all n in Z if a(n) is treated as sgn(n).
Sum_{k<0} a(k) * x^k = 1 / (1 - x) if abs(x) > 1. (End)
Dirichlet g.f.: zeta(s) - 1. - Álvar Ibeas, Nov 29 2015; corrected by Francois Oger, Oct 26 2019
E.g.f.: e^x - 1. - Francois Oger, Oct 26 2019
a(n) = 1-A000007(n). - Chai Wah Wu, Nov 14 2022
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
MATHEMATICA
Table[Sign[n], {n, 0, 104}] (* Arkadiusz Wesolowski, Sep 16 2012 *)
(* Alternative: *)
CoefficientList[Series[x/((1 - x)), {x, 0, 25}], x]
(* Alternative: *)
LinearRecurrence[{1, 0}, {0, 1}, 105]
(* Alternative: *)
Array[Sign, 105, 0]
(* Alternative: *)
N[1/9, 111]
PadRight[{0}, 120, 1] (* Harvey P. Dale, Jan 07 2023 *)
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
(Python)
def A057427(n): return int(n!=0) # Chai Wah Wu, Nov 14 2022
CROSSREFS
KEYWORD
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