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A030130 Binary expansion contains a single 0. 11
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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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 *)

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

Cf. A000918, A023416, A036563, A055010, A086224, A140977, A160502, A164874.

Sequence in context: A329569 A140144 A328893 * A164874 A337498 A045845

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 October 28 04:06 EDT 2020. Contains 338048 sequences. (Running on oeis4.)