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A007088
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Numbers written in base 2.
(Formerly M4679)
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395
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0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Or, numbers that are sums of distinct powers of 10.
Or, decimal numbers that only mention 0 and 1.
Complement of A136399; A064770(a(n)) = a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2007
a(A000290(n)) = A001737(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2009]
Contribution from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 25 2009: (Start)
Nonnegative integers with no decimal digit > 1.
Thus nonnegative integers n in base 10 such that kn can be calculated by normal addition (i.e., n + n + ... + n, with k n's (but not necessarily k + k + ... + k, with n k's)) or multiplication without requiring any carry operations for 0 <= k <= 9. (End)
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REFERENCES
| Manfred R. Schroeder, "Fractals, Chaos, Power Laws", W.H. Freeman, 1991, p. 383.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Franklin T. Adams-Watters, Table of n, a(n) for n = 0..8192
N. J. A. Sloane, Table of a(n) for n = 0..1048576
Index entries for sequences related to binary expansion of n
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FORMULA
| a(n)=Sum{d(i)*10^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n.
a(n)=(1/2)*sum(i => 0, (1-(-1)^floor(n/2^i))*10^i). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 20 2001
a(n) = A097256(n)/9.
a(2n) = 10*a(n), a(2n+1) = a(2n)+1.
G.f. 1/(1-x) * Sum_{k>=0} 10^k * x^{2^k}/(1+x^{2^k}) - for sequence as decimal integers. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2006
a(n)=Sum_k>=0 {A030308(n,k)*10^k}. - From DELEHAM Philippe, Oct 19 2011.
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EXAMPLE
| a(6)=110 because (1/2)*((1-(-1)^6)*10^0+(1-(-1)^3)*10^1+(1-(-1)^1)*10^2) = 10+100
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MAPLE
| A007088 := proc(n) local dgs ; dgs := convert(n, base, 2) ; add( op(i, dgs)*10^(i-1), i=1..nops(dgs)) ; end: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009]
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MATHEMATICA
| Table[ FromDigits[ IntegerDigits[n, 2]], {n, 0, 39}]
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PROG
| (PARI) a(n)=subst(Pol(binary(n)), x, 10)
(PARI) a(n)=if(n<=0, 0, n%2+10*a(n\2))
(Haskell)
a007088 0 = 0
a007088 n = 10 * a007088 n' + m where (n', m) = divMod n 2
-- Reinhard Zumkeller, Jan 10 2012
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CROSSREFS
| The basic sequences concerning the binary expansion of n are this one, A000788, A000069, A001969, A023416, A059015, A000120. Bisections A099820 and A099821.
Cf. A000042, A007089, A007090, A007091, A007092, A007093, A007094 & A007095.
Cf. A000695, A005836, A033042-A033052.
Cf. A159918. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2009]
Cf. A004290, A169965, A169966, A169967, A169964, A204093, A204094, A204095, A097256.
Sequence in context: A153069 A178569 A081551 * A115848 A136814 A136809
Adjacent sequences: A007085 A007086 A007087 * A007089 A007090 A007091
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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