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A004744
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Numbers whose binary expansion does not contain 011.
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9
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 48, 49, 50, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85, 96, 97, 98, 100, 101, 104, 105
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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Sum_{n>=2} 1/a(n) = 6.084750966700965350831194838591995529232464122788387705746226526437263331240... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022
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MATHEMATICA
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Select[Range[0, 110], !MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {0, 1, 1}]&] (* Harvey P. Dale, Oct 15 2013 *)
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PROG
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(PARI) is(n)=n=binary(n); for(i=3, #n, if(n[i]&&n[i-1]&&!n[i-2], return(0))); 1 \\ Charles R Greathouse IV, Mar 26 2013
(Haskell)
a004744 n = a004744_list !! (n-1)
a004744_list = filter f [0..] where
f x = x < 4 || x `mod` 8 /= 3 && f (x `div` 2)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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