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A004745
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Numbers whose binary expansion does not contain 001.
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8
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0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 40, 42, 43, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 80, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 104, 106, 107, 108, 109, 110
(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) = 5.808784664093998434778841785199192904637860758506854276321167162567685504669... (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], ! StringContainsQ[IntegerString[#, 2], "001"] &] (* Amiram Eldar, Feb 13 2022 *)
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PROG
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(PARI) is(n)=n=binary(n); for(i=4, #n, if(n[i]&&!n[i-1]&&!n[i-2], return(0))); 1 \\ Charles R Greathouse IV, Mar 29 2013
(Haskell)
a004745 n = a004745_list !! (n-1)
a004745_list = filter f [0..] where
f x = x < 4 || x `mod` 8 /= 1 && 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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