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A030130 Binary expansion contains a single 0. 12
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; text; internal format)
OFFSET
1,2
COMMENTS
From Reinhard Zumkeller, 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. - Zak Seidov, Aug 06 2010
LINKS
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. - Ulrich Schimke (ulrschimke(AT)aol.com)
a(n+1) = A140977(a(n)) for any n > 1. - Rémy Sigrist, Feb 06 2020
Sum_{n>=2} 1/a(n) = A160502. - Amiram Eldar, Oct 06 2020
EXAMPLE
23 is OK because it is '10111' in base 2.
MATHEMATICA
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 *)
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); }
(Haskell)
a030130 n = a030130_list !! (n-1)
a030130_list = filter ((== 1) . a023416) [0..]
-- Reinhard Zumkeller, Mar 31 2015, Dec 07 2012
(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
CROSSREFS
Sequence in context: A329569 A140144 A328893 * A164874 A337498 A045845
KEYWORD
nonn,base,easy,look
AUTHOR
Toby Donaldson (tjdonald(AT)uwaterloo.ca)
EXTENSIONS
More terms from Erich Friedman
Offset fixed by Reinhard Zumkeller, Aug 24 2009
STATUS
approved

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Last modified March 19 06:29 EDT 2024. Contains 370953 sequences. (Running on oeis4.)