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A089633 Numbers having not more than one 0 in their binary representation. 20
0, 1, 2, 3, 5, 6, 7, 11, 13, 14, 15, 23, 27, 29, 30, 31, 47, 55, 59, 61, 62, 63, 95, 111, 119, 123, 125, 126, 127, 191, 223, 239, 247, 251, 253, 254, 255, 383, 447, 479, 495, 503, 507, 509, 510, 511, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022, 1023 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A023416(a(n))<=1; A023416(a(n))=A023532(n-2) for n>1;

A000120(a(u))<=A000120(a(v)) for u<v; A000120(a(n))=A003056(n).

Complement of A158582. - Reinhard Zumkeller, Apr 16 2009

Also union of A168604 and A030130. - Douglas Latimer, Jul 19 2012

Numbers of the form 2^t - 2^k - 1, 0 <= k < t.

A029931(a(n)) = n and A029931(m) != n for m < a(n). - Reinhard Zumkeller, Feb 28 2014

A265705(a(n),k) = A265705(a(n),a(n)-k), k = 0 .. a(n). - Reinhard Zumkeller, Dec 15 2015

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Vladimir Shevelev, On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure, arXiv:math.CO/0801.0072. See Section 14.

V. Shevelev, Binomial Coefficient Predictors, Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.8

Vladimir Shevelev, The number of permutations with prescribed up-down structure as a function of two variables, INTEGERS, 12 (2012), #A1.

Index entries for sequences related to binary expansion of n

FORMULA

a(0)=0, n>0: a(n+1) = Min{m>n: BinOnes(a(n))<=BinOnes(m)} with BinOnes=A000120.

If m = floor((sqrt(8*n+1) - 1) / 2), then a(n) = 2^(m+1) - 2^(m*(m+3)/2 - n) - 1. - Carl R. White, Feb 10 2009

EXAMPLE

From Tilman Piesk, May 09 2012: (Start)

This may also be viewed as a triangle:             In binary:

                  0                                         0

               1     2                                 01       10

             3    5    6                          011      101      110

           7   11   13   14                  0111     1011     1101     1110

        15   23   27   29   30          01111    10111    11011    11101    11110

      31  47   55   59   61   62

   63   95  111  119  123  125  126

Left three diagonals are A000225,  A055010, A086224. Right diagonal is A000918. Central column is A129868. Numbers in row n (counted from 0) have n binary 1s. (End)

MATHEMATICA

fQ[n_] := DigitCount[n, 2, 0] < 2; Select[ Range[0, 2^10], fQ] (* Robert G. Wilson v, Aug 02 2012 *)

PROG

(Haskell)

a089633 n = a089633_list !! (n-1)

a089633_list = [2 ^ t - 2 ^ k - 1 | t <- [1..], k <- [t-1, t-2..0]]

-- Reinhard Zumkeller, Feb 23 2012

(PARI) {insq(n) = local(dd, hf, v); v=binary(n); hf=length(v); dd=sum(i=1, hf, v[i]); if(dd<=hf-2, -1, 1)}

{for(w=0, 1536, if(insq(w)>=0, print1(w, ", ")))}

\\\ Douglas Latimer, May 07 2013

CROSSREFS

Cf. A007088, A011371.

Cf. A181741 (primes), union of A081118 and A000918, apart from initial -1.

Cf. A265705.

Sequence in context: A080980 A134669 A053328 * A003172 A053329 A260442

Adjacent sequences:  A089630 A089631 A089632 * A089634 A089635 A089636

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Jan 01 2004

STATUS

approved

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Last modified June 27 21:39 EDT 2017. Contains 288804 sequences.