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A135528
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1, then repeat 1,0.
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10
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1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
(list;
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internal format)
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OFFSET
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1,1
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COMMENTS
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This is Guy Steele's sequence GS(2, 1) (see A135416).
2-adic expansion of 1/3 (right to left): 1/3 = ...01010101010101011. - Philippe Deléham, Mar 24 2009
Appears to be the Gilbreath transform of 1,2,3,5,7,11,13,... (A008578). (This is essentially the same as the Gilbreath conjecture, see A036262.) - N. J. A. Sloane, May 08 2023
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LINKS
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FORMULA
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G.f.: x / (1 - x / (1 + x / (1 + x / (1 - x)))). - Michael Somos, Apr 02 2012
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EXAMPLE
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G.f. = x + x^2 + x^4 + x^6 + x^8 + x^10 + x^12 + x^14 + x^16 + x^18 + x^20 + ...
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
a135528 n = a135528_list !! (n-1)
a135528_list = concat $ iterate ([1, 0] *) [1]
instance Num a => Num [a] where
fromInteger k = [fromInteger k]
(p:ps) + (q:qs) = p + q : ps + qs
ps + qs = ps ++ qs
(0:ps) * qs = 0 : ps * qs
(p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
_ * _ = []
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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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STATUS
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approved
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