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A165754
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a(n) = nimsum(n+(n+1)+(n+2)).
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1
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3, 0, 5, 2, 7, 4, 9, 6, 11, 8, 13, 10, 15, 12, 17, 14, 19, 16, 21, 18, 23, 20, 25, 22, 27, 24, 29, 26, 31, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 43, 40, 45, 42, 47, 44, 49, 46, 51, 48, 53, 50, 55, 52, 57, 54, 59, 56, 61, 58, 63, 60, 65, 62, 67, 64, 69, 66, 71, 68, 73, 70
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OFFSET
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0,1
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COMMENTS
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Start with 3. Then repeat the cycle: subtract 3, add 5. The odd-indexed terms give the odd numbers, beginning with 3. The even-indexed terms give the even numbers, beginning with 0. In the infinite sequence, every positive integer except 1 is listed.
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.
G.f.: (2*x^2-3*x+3) / ((x-1)^2*(x+1)). (End)
Sum_{n>=2} (-1)^(n+1)/a(n) = 4/3 - log(2). - Amiram Eldar, Sep 10 2023
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EXAMPLE
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For n = 3, Nimsum(3 + 4 + 5) = 2, as shown: 011 XOR 100 XOR 101 010.
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MAPLE
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read("transforms") ; A165754 := proc(n) nimsum(nimsum(n, n+1), n+2) ; end: seq(A165754(n), n=0..120) ; # R. J. Mathar, Sep 28 2009
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MATHEMATICA
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Flatten[NestList[{Last[#]+5, Last[#]+2}&, {3, 0}, 40]] (* Harvey P. Dale, Dec 04 2011 *)
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PROG
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(Python)
n = 0
while n < 100:
print(n^(n+1)^(n+2), end=', ')
n += 1
(PARI) Vec((2*x^2-3*x+3)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009
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EXTENSIONS
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STATUS
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approved
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