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A115638
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A Jacobsthal-related divide-and-conquer sequence.
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2
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1, -1, 5, -1, -3, -1, 21, -1, -3, -1, -11, -1, -3, -1, 85, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, 341, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, -171, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, 1365, -1, -3, -1, -11, -1, -3, -1, -43
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} 4^k*x^(2^(k+1)-2)/(1+x^(2^k)); the g.f. G(x) satisfies G(x) - 4*x^2*G(x^2) = 1/(1+x).
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MATHEMATICA
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A115637[n_] := FromDigits[1 - IntegerDigits[n + 2, 2], 4];
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PROG
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(Python)
def A115638(n): return int(bin((~(n+2))^(-1<<(n+2).bit_length()))[2:], 4)-int(bin((~(n+1))^(-1<<(n+1).bit_length()))[2:], 4) # Chai Wah Wu, Jul 17 2024
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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