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A089633
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Numbers having not more than one 0 in their binary representation.
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20
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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
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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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
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FORMULA
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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
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EXAMPLE
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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)
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MATHEMATICA
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fQ[n_] := DigitCount[n, 2, 0] < 2; Select[ Range[0, 2^10], fQ] (* Robert G. Wilson v, Aug 02 2012 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Jan 01 2004
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STATUS
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approved
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