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A325910
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a(n) = ( (-1)^(n-1) * Sum_{k=0..n-1} (-1)^k*10^(2^k) - (1-(-1)^n)/2 )/9.
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7
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = -a(n-1) + (10^(2^(n-1)) - 1)/9.
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EXAMPLE
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1 = -0 + 1.
10 = -1 + 11.
1101 = -10 + 1111.
11110010 = -1101 + 11111111.
1111111100001101 = -11110010 + 1111111111111111.
================================================
--+------------------------------+-------------
1 | 1 = 1 | 2
2 | (10)_2 = 2 | 2
3 | (1101)_2 = 13 | 14
4 | (11110010)_2 = 242 | 242
5 | (1111111100001101)_2 = 65293 | 65294
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MATHEMATICA
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a[n_] := ((-1)^(n - 1) * Sum[(-1)^k * 10^(2^k), {k, 0, n - 1} ] - (1 - (-1)^n)/2)/9; Array[a, 8, 0] (* Amiram Eldar, May 07 2021 *)
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PROG
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(PARI) {a(n) = ((-1)^(n-1)*sum(k=0, n-1, (-1)^k*10^2^k)-(1-(-1)^n)/2)/9}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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