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A030130
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Binary expansion contains a single 0.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2009: (Start)
A023416(a(n)) = 1;
apart from the initial term the sequence can be seen as a triangle read by rows, see A164874;
A055010 and A086224 are subsequences, see also A000918 and A036563. (End)
Zero and numbers of form 2^m-2^k-1, 2<=m, 0<=k<=m-2. [From Zak Seidov (zakseidov(AT)yahoo.com), Aug 06 2010]
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..1000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2009]
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FORMULA
| 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 - UlrSchimke(AT)aol.com.
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EXAMPLE
| 23 is OK because it is '10111' in base 2.
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MATHEMATICA
| Sort[Flatten[{{0}, Table[2^n - 2^m - 1, {n, 2, 50}, {m, 0, n - 2}]}]] [From Zak Seidov (zakseidov(AT)yahoo.com), Aug 06 2010]
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PROG
| (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); }
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CROSSREFS
| Sequence in context: A026344 A057812 A140144 * A164874 A045845 A002133
Adjacent sequences: A030127 A030128 A030129 * A030131 A030132 A030133
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KEYWORD
| nonn,base,easy
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AUTHOR
| Toby Donaldson (tjdonald(AT)uwaterloo.ca)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
Offset fixed by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 24 2009
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