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 A281098 a(n) is the GCD of the sequence d(n) = A261327(k+n) - A261327(k) for all k. 1
 0, 1, 1, 3, 4, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 3, 16, 1, 9, 1, 20, 3, 11, 1, 24, 1, 13, 3, 28, 1, 15, 1, 32, 3, 17, 1, 36, 1, 19, 3, 40, 1, 21, 1, 44, 3, 23, 1, 48, 1, 25, 3, 52, 1, 27, 1, 56, 3, 29, 1, 60, 1, 31, 3, 64, 1, 33, 1, 68, 3, 35, 1, 72, 1, 37, 3, 76, 1, 39, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Successive sequences: 0: 0, 0, 0, 0, ... = 0 * ( ) 1: 4, -3, 11, -8, ... = 1 * ( ) 2: 1, 8, 3, 16, ... = 1 * ( ) A195161 3: 12, 0, 27, -3, ... = 3 * (4, 0, 9, -1, ...) 4: 4, 24, 8, 40, ... = 4 * (1, 6, 2, 10, ...) A064680 5; 28, 5, 51, 4, ... = 1 * ( ) 6: 9, 48, 15, 72, ... = 3 * (3, 16, 5, 24, ...) A195161 7: 52, 12, 83, 13, ... = 1 * ( ) 8: 16, 80, 24, 112, ... = 8 * (2, 10, 3, 14, ...) A064080 9: 84 21, 123, 24, ... = 3 * (28, 7, 41, 8, ...) 10: 25, 120, 35, 160, ... = 5 * (5, 24, 7, 32, ...) A195161 LINKS Antti Karttunen, Table of n, a(n) for n = 0..16384 Index entries for linear recurrences with constant coefficients, signature (0,-1,0,1,0,2,0,1,0,-1,0,-1). FORMULA G.f.: -x*( -1 - x - 4*x^2 - 5*x^3 - 3*x^4 - 6*x^5 + 3*x^6 - 5*x^7 + 4*x^8 - x^9 + x^10 )/( (x^2 - x + 1)*(1 + x + x^2)*(x - 1)^2*(1 + x)^2*(1 + x^2)^2 ). - R. J. Mathar, Jan 31 2017 a(2*k) = A022998(k). a(2*k+1) = A109007(k-1). a(3*k) = interleave 3*k*(3 +(-1)^k)/2, 3. a(3*k+1) = interleave 1, A166304(k). a(3*k+2) = interleave A166138(k), 1. a(4*k) = 4*k. a(4*k+1) = period 3: repeat [1, 1, 3]. a(4*k+2) = 1 + 2*k. a(4*k+3) = period 3: repeat [3, 1, 1]. a(n+12) - a(n) = 6*A131743(n+3). a(n) = (18*n + 40 - 16*cos(n*Pi/3) + 9*n*cos(n*Pi/2) + 32*cos(2*n*Pi/3) + (18*n - 40)*cos(n*Pi) + 3*n*cos(3*n*Pi/2) - 16*cos(5*n*Pi/3))/48. - Wesley Ivan Hurt, Oct 04 2018 MATHEMATICA CoefficientList[Series[(-x (-1 - x - 4 x^2 - 5 x^3 - 3 x^4 - 6 x^5 + 3 x^6 - 5 x^7 + 4 x^8 - x^9 + x^10))/((x^2 - x + 1) (1 + x + x^2) (x - 1)^2*(1 + x)^2*(1 + x^2)^2), {x, 0, 79}], x] (* Michael De Vlieger, Feb 02 2017 *) PROG (PARI) f(n) = numerator((4 + n^2)/4); a(n) = gcd(vector(1000, k, f(k+n) - f(k))); \\ Michel Marcus, Jan 15 2017 (PARI) A281098(n) = if(n%2, gcd((n\2)-1, 3), n>>(bitand(n, 2)/2)); \\ Antti Karttunen, Feb 15 2023 CROSSREFS Cf. A064680, A144433 or A195161. Cf. A000012, A005408, A008586, A010701, A109007 (bisection), A016825, A165988 (via A022998), A166138, A166304, A280579. Sequence in context: A124909 A348354 A356708 * A090279 A101667 A117378 Adjacent sequences: A281095 A281096 A281097 * A281099 A281100 A281101 KEYWORD nonn,easy AUTHOR Paul Curtz, Jan 14 2017 EXTENSIONS Corrected and extended by Michel Marcus, Jan 15 2017 STATUS approved

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Last modified July 14 22:52 EDT 2024. Contains 374323 sequences. (Running on oeis4.)