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A030130
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Binary expansion contains a single 0.
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12
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0, 2, 5, 6, 11, 13, 14, 23, 27, 29, 30, 47, 55, 59, 61, 62, 95, 111, 119, 123, 125, 126, 191, 223, 239, 247, 251, 253, 254, 383, 447, 479, 495, 503, 507, 509, 510, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022, 1535, 1791, 1919, 1983, 2015, 2031, 2039
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OFFSET
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1,2
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COMMENTS
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apart from the initial term the sequence can be seen as a triangle read by rows, see A164874;
Zero and numbers of form 2^m-2^k-1, 2 <= m, 0 <= k <= m-2. - Zak Seidov, Aug 06 2010
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LINKS
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FORMULA
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a(n) = 2^(g(n))-1-2^(((2*g(n)-1)^2-1-8*n)/8) with g(n)=int((sqrt(8*n-7)+3)/2) for all n>0 and g(0)=1. - Ulrich Schimke (ulrschimke(AT)aol.com)
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EXAMPLE
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23 is OK because it is '10111' in base 2.
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MATHEMATICA
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Sort[Flatten[{{0}, Table[2^n - 2^m - 1, {n, 2, 50}, {m, 0, n - 2}]}]] (* Zak Seidov, Aug 06 2010 *)
Select[Range[0, 2100], DigitCount[#, 2, 0]==1&] (* Harvey P. Dale, Dec 19 2021 *)
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PROG
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(C) long int element (long int i) { return (pow(2, g(i))-1-pow(2, (pow(2*g(i)-1, 2)-1-8*i)/8)); } long int g(long int m) {if (m==0) return(1); return ((sqrt(8*m-7)+3)/2); }
(Haskell)
a030130 n = a030130_list !! (n-1)
a030130_list = filter ((== 1) . a023416) [0..]
(PARI) print1("0, "); for(k=1, 2039, my(v=digits(k, 2)); if(vecsum(v)==#v-1, print1(k, ", "))) \\ Hugo Pfoertner, Feb 06 2020
(Magma) [0] cat [k:k in [0..2050]| Multiplicity(Intseq(k, 2), 0) eq 1]; // Marius A. Burtea, Feb 06 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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Toby Donaldson (tjdonald(AT)uwaterloo.ca)
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EXTENSIONS
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STATUS
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approved
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