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 A253513 The characteristic function of the multiples of eight. 4
 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Period 8: repeat [1, 0, 0, 0, 0, 0, 0, 0]. LINKS Antti Karttunen, Table of n, a(n) for n = 0..16384 Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1). FORMULA a(n) = floor(n/8) - floor((n-1)/8). a(n) = sin((sin(Pi*(n+1)/2)^2)*Pi*(n+2)/4)/2 + (sin(Pi*(n+1)/2)^2)/4 + sin(Pi*(n+1)/2)/4. a(n) = abs(A014025(n)). From Alois P. Heinz, Jan 03 2015: (Start) a(n) = 1 - A168181(n). G.f.: 1/(1-x^8). (End) MATHEMATICA Table[Boole[IntegerQ[n/8]], {n, 0, 127}] (* Michael De Vlieger, Jan 03 2015, after Alonso del Arte at A121262 *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0}, 120] (* or *) PadRight[ {}, 120, {1, 0, 0, 0, 0, 0, 0, 0}] (* Harvey P. Dale, Apr 07 2017 *) Array[ Boole[ Mod[#, 8] == 0] &, 105, 0] (* Robert G. Wilson v, Oct 08 2017 *) PROG (PARI) A253513(n) = !(n%8); \\ Antti Karttunen, Oct 08 2017 CROSSREFS Cf. A008590 (multiples of 8), A010877, A014025, A168181, A244413. Sequence in context: A104124 A052434 A015241 * A014025 A279760 A287457 Adjacent sequences:  A253510 A253511 A253512 * A253514 A253515 A253516 KEYWORD nonn,easy AUTHOR Mikael Aaltonen, Jan 03 2015 STATUS approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)