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A030130 Binary expansion contains a single 0. 10
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

R. Zumkeller, Table of n, a(n) for n = 1..1000 [From Reinhard Zumkeller, Aug 29 2009]

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)

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 *)

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

CROSSREFS

Cf. A023416, A164874, A055010, A086224, A000918, A036563.

Sequence in context: A026344 A057812 A140144 * A164874 A045845 A002133

Adjacent sequences:  A030127 A030128 A030129 * A030131 A030132 A030133

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 25 01:30 EDT 2017. Contains 284036 sequences.