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A057427 a(n) = 1 if n > 0, a(n) = 0 if n = 0; series expansion of x/(1-x).

%I A057427 #179 Jan 07 2023 12:39:24
%S A057427 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,
%T A057427 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,
%U A057427 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
%N A057427 a(n) = 1 if n > 0, a(n) = 0 if n = 0; series expansion of x/(1-x).
%C A057427 Parity of (n+1)-st prime, A000040(n+1). - _Philippe Deléham_, Apr 04 2009
%C A057427 Decimal expansion of 1/90.
%C A057427 Partial sums of A063524 (characteristic function of 1). - _Jeremy Gardiner_, Sep 08 2002
%C A057427 Characteristic function of positive integers. - _Franklin T. Adams-Watters_, Aug 01 2011
%C A057427 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
%C A057427 Central terms of the triangle in A152487. - _Reinhard Zumkeller_, Dec 06 2008
%C A057427 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.
%D A057427 T. M. MacRobert, Functions of a Complex Variable, 4th ed., Macmillan and Co., London, 1958, p. 90.
%H A057427 Vincenzo Librandi, <a href="/A057427/b057427.txt">Table of n, a(n) for n = 0..200</a>
%H A057427 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H A057427 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A057427 G.f.: x / (1 - x).
%F A057427 G.f.: Sum_{k>=0} 2^k * x^(2^k) / (1 + x^(2^k)). - _Michael Somos_, Sep 11 2005
%F A057427 a(A000027(n)) = 1; a(A000004(n)) = 0. - _Reinhard Zumkeller_, Oct 11 2008
%F A057427 a(n) = A000007(0^n). - _Jaume Oliver Lafont_, Mar 19 2009
%F A057427 From _Michael Somos_, Aug 17 2015: (Start)
%F A057427 a(n) = -a(-n) for all n in Z if a(n) is treated as sgn(n).
%F A057427 Sum_{k<0} a(k) * x^k = 1 / (1 - x) if abs(x) > 1. (End)
%F A057427 Dirichlet g.f.: zeta(s) - 1. - _Álvar Ibeas_, Nov 29 2015; corrected by _Francois Oger_, Oct 26 2019
%F A057427 a(n) = A001065(n+1) - A048050(n+1). - _Omar E. Pol_, Apr 30 2018
%F A057427 E.g.f.: e^x - 1. - _Francois Oger_, Oct 26 2019
%F A057427 a(n) = 1-A000007(n). - _Chai Wah Wu_, Nov 14 2022
%e A057427 1/90 = .0111111111111111111...
%e A057427 G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + ...
%p A057427 A057427:= signum: seq(A057427(k), k=0..50); # _Wesley Ivan Hurt_, Oct 22 2013
%t A057427 Table[Sign[n], {n, 0, 104}] (* _Arkadiusz Wesolowski_, Sep 16 2012 *)
%t A057427 CoefficientList[Series[x/((1 - x)), {x, 0, 25}], x]
%t A057427 LinearRecurrence[{1, 0}, {0, 1}, 105]
%t A057427 Array[Sign, 105, 0]
%t A057427 N[1/9, 111]
%t A057427 PadRight[{0},120,1] (* _Harvey P. Dale_, Jan 07 2023 *)
%o A057427 (PARI) {a(n) = sign(n)};
%o A057427 (PARI) /* n>=0 */ a(n)=!!n \\ _Jaume Oliver Lafont_, Mar 19 2009
%o A057427 (Haskell)
%o A057427 a057427 = signum
%o A057427 a057427_list = 0 : [1, 1 ..]  -- _Reinhard Zumkeller_, Nov 28 2012
%o A057427 (Python)
%o A057427 def A057427(n): return int(n!=0) # _Chai Wah Wu_, Nov 14 2022
%Y A057427 Cf. A000004, A000007, A000012, A000027, A000040, A063524, A152487.
%Y A057427 See also A261012.
%K A057427 nonn,easy,mult,nice,cons
%O A057427 0,1
%A A057427 _Henry Bottomley_, Sep 05 2000
%E A057427 Entry edited at the suggestion of _Robert G. Wilson v_ by _N. J. A. Sloane_, Aug 16 2015